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<h2 id="automated-planning">Automated planning</h2> <p class="note">Further information: <a href="/facts/List_of_algorithms_for_automated_planning/VL1TcrmD">List of algorithms for automated planning</a></p> <h2 id="combinatorial-algorithms">Combinatorial algorithms</h2> <p class="note">Further information: <a href="/facts/Combinatorics/k14xUoKT">Combinatorics</a></p> <h3>General combinatorial algorithms</h3> <ul><li><a href="/facts/Cycle_detection/S1dA6pJr">Brent's algorithm</a>: finds a cycle in function value iterations using only two iterators<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a></li> <li><a href="/facts/Floyd%2527s_cycle-finding_algorithm/S1dA6pJr">Floyd's cycle-finding algorithm</a>: finds a cycle in function value iterations<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a></li> <li><a href="/facts/Gale%25E2%2580%2593Shapley_algorithm/J6Cv94B7">Gale–Shapley algorithm</a>: solves the <a href="/facts/Stable_matching_problem/tzNRpF1f">stable matching problem</a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></li> <li><a href="/facts/Pseudorandom_number_generator/sIrCxIBq">Pseudorandom number generators</a> (uniformly distributed—see also <a href="/facts/List_of_random_number_generators/oWbCuAdA">List of pseudorandom number generators</a> for other PRNGs with varying degrees of convergence and varying statistical quality): <ul><li><a href="/facts/ACORN_(PRNG)/FJDJggWV">ACORN generator</a></li> <li><a href="/facts/Blum_Blum_Shub/aWEKXsnX">Blum Blum Shub</a></li> <li><a href="/facts/Lagged_Fibonacci_generator/UeeQr5Uf">Lagged Fibonacci generator</a></li> <li><a href="/facts/Linear_congruential_generator/E4PyJQ5U">Linear congruential generator</a></li> <li><a href="/facts/Mersenne_Twister/R6Knca0q">Mersenne Twister</a></li></ul></li></ul> <h3>Graph algorithms</h3> <p class="note">Further information: Category:Graph algorithms and <a href="/facts/Graph_theory/VVPCd4TX">Graph theory</a></p> <ul><li><a href="/facts/Coloring_algorithm/J6HoBfP0">Coloring algorithm</a>: Graph coloring algorithm.</li> <li><a href="/facts/Hopcroft%25E2%2580%2593Karp_algorithm/fEGdr2VP">Hopcroft–Karp algorithm</a>: convert a bipartite graph to a <a href="/facts/Maximum_cardinality_matching/oKaChmBt">maximum cardinality matching</a></li> <li><a href="/facts/Hungarian_algorithm/rRCJebc1">Hungarian algorithm</a>: algorithm for finding a <a href="/facts/Perfect_matching/LmtRYLgK">perfect matching</a></li> <li><a href="/facts/Pr%25C3%25BCfer_sequence/0tmI33Mm">Prüfer coding</a>: conversion between a labeled tree and its <a href="/facts/Pr%25C3%25BCfer_sequence/0tmI33Mm">Prüfer sequence</a></li> <li><a href="/facts/Tarjan%2527s_off-line_lowest_common_ancestors_algorithm/mTf59kmP">Tarjan's off-line lowest common ancestors algorithm</a>: computes <a href="/facts/Lowest_common_ancestor/lUuLKAGk">lowest common ancestors</a> for pairs of nodes in a tree</li> <li><a href="/facts/Topological_sorting/VY7gNtYA">Topological sort</a>: finds linear order of nodes (e.g. jobs) based on their dependencies.</li></ul> <h4>Graph drawing</h4> <p class="note">Further information: <a href="/facts/Graph_drawing/uhh73BVo">Graph drawing</a></p> <ul><li><a href="/facts/Force-based_algorithms_(graph_drawing)/CWAwEwXW">Force-based algorithms</a> (also known as force-directed algorithms or spring-based algorithm)</li> <li><a href="/facts/Spectral_layout/vJ1BMtKC">Spectral layout</a></li></ul> <h4>Network theory</h4> <p class="note">Further information: <a href="/facts/Network_theory/m6CQovwm">Network theory</a></p> <ul><li>Network analysis <ul><li>Link analysis <ul><li><a href="/facts/Girvan%25E2%2580%2593Newman_algorithm/zo2fvBST">Girvan–Newman algorithm</a>: detect communities in complex systems</li> <li>Web link analysis <ul><li><a href="/facts/Hyperlink-Induced_Topic_Search/QpTGWgub">Hyperlink-Induced Topic Search</a> (HITS) (also known as <a href="/facts/Hubs_and_authorities/QpTGWgub">Hubs and authorities</a>)</li> <li><a href="/facts/PageRank/KtJRJFUX">PageRank</a></li> <li><a href="/facts/TrustRank/P8ovtsWl">TrustRank</a></li></ul></li></ul></li></ul></li> <li><a href="/facts/Flow_network/k0LCoRwD">Flow networks</a> <ul><li><a href="/facts/Dinic%2527s_algorithm/n8yqcENs">Dinic's algorithm</a>: is a <a href="/facts/Strongly_polynomial/77T62gmf">strongly polynomial</a> algorithm for computing the <a href="/facts/Maximum_flow/aSal0FGF">maximum flow</a> in a <a href="/facts/Flow_network/k0LCoRwD">flow network</a>.</li> <li><a href="/facts/Edmonds%25E2%2580%2593Karp_algorithm/GvH0Q88t">Edmonds–Karp algorithm</a>: implementation of Ford–Fulkerson</li> <li><a href="/facts/Ford%25E2%2580%2593Fulkerson_algorithm/wwk3tw52">Ford–Fulkerson algorithm</a>: computes the <a href="/facts/Maximum_flow_problem/aSal0FGF">maximum flow</a> in a graph</li> <li><a href="/facts/Karger%2527s_algorithm/D58kwvgc">Karger's algorithm</a>: a Monte Carlo method to compute the <a href="/facts/Minimum_cut/xWTNp1hN">minimum cut</a> of a connected graph</li> <li><a href="/facts/Push%25E2%2580%2593relabel_algorithm/MaSvQkmo">Push–relabel algorithm</a>: computes a <a href="/facts/Maximum_flow_problem/aSal0FGF">maximum flow</a> in a graph</li></ul></li></ul> <h4>Routing for graphs</h4> <ul><li><a href="/facts/Edmonds%2527_algorithm/tu1FE4B2">Edmonds' algorithm</a> (also known as Chu–Liu/Edmonds' algorithm): find maximum or minimum branchings</li> <li><a href="/facts/Euclidean_minimum_spanning_tree/yu6atHA6">Euclidean minimum spanning tree</a>: algorithms for computing the minimum spanning tree of a set of points in the plane</li> <li><a href="/facts/Longest_path_problem/W17hlDKs">Longest path problem</a>: find a simple path of maximum length in a given graph</li> <li><a href="/facts/Minimum_spanning_tree/kgkGmY9s">Minimum spanning tree</a> <ul><li><a href="/facts/Bor%25C5%25AFvka%2527s_algorithm/Hs1pkNRB">Borůvka's algorithm</a></li> <li><a href="/facts/Kruskal%2527s_algorithm/sg8v1BHB">Kruskal's algorithm</a></li> <li><a href="/facts/Prim%2527s_algorithm/UHEcY2lH">Prim's algorithm</a></li> <li><a href="/facts/Reverse-delete_algorithm/Psc5hj0h">Reverse-delete algorithm</a></li></ul></li> <li><a href="/facts/Nonblocking_minimal_spanning_switch/5MmWMNvp">Nonblocking minimal spanning switch</a> say, for a <a href="/facts/Telephone_exchange/PaRpGm8I">telephone exchange</a></li> <li><a href="/facts/Shortest_path_problem/g4nsrswr">Shortest path problem</a> <ul><li><a href="/facts/Bellman%25E2%2580%2593Ford_algorithm/Sx6INcdr">Bellman–Ford algorithm</a>: computes <a href="/facts/Shortest_path_problem/g4nsrswr">shortest paths</a> in a weighted graph (where some of the edge weights may be negative)</li> <li><a href="/facts/Dijkstra%2527s_algorithm/ehun88jl">Dijkstra's algorithm</a>: computes <a href="/facts/Shortest_path_problem/g4nsrswr">shortest paths</a> in a graph with non-negative edge weights</li> <li><a href="/facts/Floyd%25E2%2580%2593Warshall_algorithm/fo2XUseS">Floyd–Warshall algorithm</a>: solves the <a href="/facts/Shortest_path_problem/g4nsrswr">all pairs shortest path</a> problem in a weighted, directed graph</li> <li><a href="/facts/Johnson%2527s_algorithm/ef7m9e3n">Johnson's algorithm</a>: all pairs shortest path algorithm in sparse weighted directed graph</li></ul></li> <li><a href="/facts/Transitive_closure/HEtgYGM4">Transitive closure</a> problem: find the <a href="/facts/Transitive_closure/HEtgYGM4">transitive closure</a> of a given binary relation</li> <li><a href="/facts/Traveling_salesman_problem/2WEKVLnV">Traveling salesman problem</a> <ul><li><a href="/facts/Christofides_algorithm/BK7nVcoL">Christofides algorithm</a></li> <li><a href="/facts/Nearest_neighbour_algorithm/EjKh21yG">Nearest neighbour algorithm</a></li></ul></li> <li><a href="/facts/Vehicle_routing_problem/TS5pWNdR">Vehicle routing problem</a> <ul><li>Clarke and Wright Saving algorithm</li></ul></li> <li><a href="/facts/Warnsdorff%2527s_rule/VuzxY4pt">Warnsdorff's rule</a>: a heuristic method for solving the <a href="/facts/Knight%2527s_tour/VuzxY4pt">Knight's tour</a> problem</li></ul> <h4>Graph search</h4> <p class="note">Further information: <a href="/facts/Graph_search_algorithm/vFjrnHxr">Graph search algorithm</a> and <a href="/facts/State_space_search/bky9oQSb">State space search</a></p> <ul><li><a href="/facts/A*_search_algorithm/BXFmt6hz">A*</a>: special case of best-first search that uses heuristics to improve speed</li> <li><a href="/facts/B*/joFfJnj6">B*</a>: a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node (out of one or more possible goals)</li> <li><a href="/facts/Backtracking/Jm9vDUk8">Backtracking</a>: abandons partial solutions when they are found not to satisfy a complete solution</li> <li><a href="/facts/Beam_search/EFPaqKkM">Beam search</a>: is a heuristic search algorithm that is an optimization of <a href="/facts/Best-first_search/jaIwMxBE">best-first search</a> that reduces its memory requirement</li> <li><a href="/facts/Beam_stack_search/LWxrtTBq">Beam stack search</a>: integrates backtracking with <a href="/facts/Beam_search/EFPaqKkM">beam search</a></li> <li><a href="/facts/Best-first_search/jaIwMxBE">Best-first search</a>: traverses a graph in the order of likely importance using a <a href="/facts/Priority_queue/1uXVo4Uf">priority queue</a></li> <li><a href="/facts/Bidirectional_search/KgobffdQ">Bidirectional search</a>: find the shortest path from an initial vertex to a goal vertex in a directed graph</li> <li><a href="/facts/Breadth-first_search/2kulDXCx">Breadth-first search</a>: traverses a graph level by level</li> <li><a href="/facts/Brute-force_search/YU2fzBIt">Brute-force search</a>: an exhaustive and reliable search method, but computationally inefficient in many applications</li> <li><a href="/facts/D*/YcsgHseH">D*</a>: an <a href="/facts/Incremental_heuristic_search/IGJCqRrl">incremental heuristic search</a> algorithm</li> <li><a href="/facts/Depth-first_search/luxJKVph">Depth-first search</a>: traverses a graph branch by branch</li> <li><a href="/facts/Dijkstra%2527s_algorithm/ehun88jl">Dijkstra's algorithm</a>: a special case of A* for which no heuristic function is used</li> <li><a href="/facts/General_Problem_Solver/r0lMBqR7">General Problem Solver</a>: a seminal theorem-proving algorithm intended to work as a universal problem solver machine.</li> <li><a href="/facts/Iterative_deepening_depth-first_search/BezFNMTR">Iterative deepening depth-first search</a> (IDDFS): a state space search strategy</li> <li><a href="/facts/Jump_point_search/qVvxxobP">Jump point search</a>: an optimization to A* which may reduce computation time by an order of magnitude using further heuristics</li> <li><a href="/facts/Lexicographic_breadth-first_search/35b5KsmM">Lexicographic breadth-first search</a> (also known as Lex-BFS): a linear time algorithm for ordering the vertices of a graph</li> <li><a href="/facts/SSS*/gVHSW170">SSS*</a>: state space search traversing a game tree in a best-first fashion similar to that of the A* search algorithm</li> <li><a href="/facts/Uniform-cost_search/ehun88jl">Uniform-cost search</a>: a <a href="/facts/Tree_traversal/Dkch34pz">tree search</a> that finds the lowest-cost route where costs vary</li></ul> <h4>Subgraphs</h4> <ul><li><a href="/facts/Clique_(graph_theory)/XK9ppLz5">Cliques</a> <ul><li><a href="/facts/Bron%25E2%2580%2593Kerbosch_algorithm/WM0FyQ2U">Bron–Kerbosch algorithm</a>: a technique for finding <a href="/facts/Maximal_clique/XK9ppLz5">maximal cliques</a> in an undirected graph</li> <li><a href="/facts/MaxCliqueDyn_maximum_clique_algorithm/zoysuADT">MaxCliqueDyn maximum clique algorithm</a>: find a <a href="/facts/Maximum_clique/XK9ppLz5">maximum clique</a> in an undirected graph</li></ul></li> <li><a href="/facts/Strongly_connected_components/P6rBqb7W">Strongly connected components</a> <ul><li><a href="/facts/Kosaraju%2527s_algorithm/MYLcDEc0">Kosaraju's algorithm</a></li> <li><a href="/facts/Path-based_strong_component_algorithm/PctG4xP4">Path-based strong component algorithm</a></li> <li><a href="/facts/Tarjan%2527s_strongly_connected_components_algorithm/N4e6cb6M">Tarjan's strongly connected components algorithm</a></li></ul></li> <li><a href="/facts/Subgraph_isomorphism_problem/86LLWRg4">Subgraph isomorphism problem</a></li></ul> <h3>Sequence algorithms</h3> <p class="note">Further information: <a href="/facts/Sequences/gV2S4uqp">Sequences</a></p> <h4>Approximate sequence matching</h4> <ul><li><a href="/facts/Bitap_algorithm/qwbnEJ6n">Bitap algorithm</a>: fuzzy algorithm that determines if strings are approximately equal.</li> <li><a href="/facts/Phonetic_algorithm/FVea6LH5">Phonetic algorithms</a> <ul><li><a href="/facts/Daitch%25E2%2580%2593Mokotoff_Soundex/YPGI9fSN">Daitch–Mokotoff Soundex</a>: a <a href="/facts/Soundex/1EL8PN6b">Soundex</a> refinement which allows matching of Slavic and Germanic surnames</li> <li><a href="/facts/Double_Metaphone/jCI2G4QG">Double Metaphone</a>: an improvement on Metaphone</li> <li><a href="/facts/Match_rating_approach/M9bKJHv8">Match rating approach</a>: a phonetic algorithm developed by Western Airlines</li> <li><a href="/facts/Metaphone/jCI2G4QG">Metaphone</a>: an algorithm for indexing words by their sound, when pronounced in English</li> <li><a href="/facts/New_York_State_Identification_and_Intelligence_System/st2teb09">NYSIIS</a>: <a href="/facts/Phonetic_algorithm/FVea6LH5">phonetic algorithm</a>, improves on <a href="/facts/Soundex/1EL8PN6b">Soundex</a></li> <li><a href="/facts/Soundex/1EL8PN6b">Soundex</a>: a phonetic algorithm for indexing names by sound, as pronounced in English</li></ul></li> <li><a href="/facts/String_metric/hAteGu4J">String metrics</a>: computes a similarity or dissimilarity (distance) score between two pairs of text strings <ul><li><a href="/facts/Damerau%25E2%2580%2593Levenshtein_distance/Y8zpLKpY">Damerau–Levenshtein distance</a>: computes a distance measure between two strings, improves on <a href="/facts/Levenshtein_distance/F0otyNSl">Levenshtein distance</a></li> <li><a href="/facts/Dice%2527s_coefficient/rwLufgya">Dice's coefficient</a> (also known as the Dice coefficient): a similarity measure related to the <a href="/facts/Jaccard_index/dUurmTet">Jaccard index</a></li> <li><a href="/facts/Hamming_distance/MgdtbYPo">Hamming distance</a>: sum number of positions which are different</li> <li><a href="/facts/Jaro%25E2%2580%2593Winkler_distance/IpG3X2FW">Jaro–Winkler distance</a>: is a measure of similarity between two strings</li> <li><a href="/facts/Levenshtein_distance/F0otyNSl">Levenshtein edit distance</a>: computes a metric for the amount of difference between two sequences</li></ul></li> <li><a href="/facts/Trigram_search/NSehMr4u">Trigram search</a>: search for text when the exact syntax or spelling of the target object is not precisely known</li></ul> <h4>Selection algorithms</h4> <p class="note">Main article: <a href="/facts/Selection_algorithm/zyxLnxNf">Selection algorithm</a></p> <ul><li><a href="/facts/Introselect/cM7BADYe">Introselect</a></li> <li><a href="/facts/Quickselect/KJmN0f4B">Quickselect</a></li></ul> <h4>Sequence search</h4> <ul><li><a href="/facts/Linear_search/cBh6w2sq">Linear search</a>: locates an item in an unsorted sequence</li> <li><a href="/facts/Selection_algorithm/zyxLnxNf">Selection algorithm</a>: finds the <i>k</i>th largest item in a sequence</li> <li><a href="/facts/Sorted_list/PwHpj1Gs">Sorted lists</a> <ul><li><a href="/facts/Binary_search_algorithm/FFmQzunc">Binary search algorithm</a>: locates an item in a sorted sequence</li> <li><a href="/facts/Eytzinger_binary_search/1ofAD9yV">Eytzinger binary search</a>: cache friendly binary search algorithm <a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></li> <li><a href="/facts/Fibonacci_search_technique/NR7432DA">Fibonacci search technique</a>: search a sorted sequence using a divide and conquer algorithm that narrows down possible locations with the aid of <a href="/facts/Fibonacci_numbers/mqxpAUQD">Fibonacci numbers</a></li> <li><a href="/facts/Jump_search/8IyEVBcP">Jump search</a> (or block search): linear search on a smaller subset of the sequence</li> <li><a href="/facts/Interpolation_search/nRtGvK4u">Predictive search</a>: binary-like search which factors in <a href="/facts/Magnitude_(mathematics)/KCn9PoF0">magnitude</a> of search term versus the high and low values in the search. Sometimes called dictionary search or interpolated search.</li> <li><a href="/facts/Uniform_binary_search/nejCa30D">Uniform binary search</a>: an optimization of the classic binary search algorithm</li></ul></li> <li><a href="/facts/Ternary_search/rMDlYnoB">Ternary search</a>: a technique for finding the minimum or maximum of a function that is either strictly increasing and then strictly decreasing or vice versa</li></ul> <h4>Sequence merging</h4> <p class="note">Main article: <a href="/facts/Merge_algorithm/pycrPFFE">Merge algorithm</a></p> <ul><li><a href="/facts/K-way_merge_algorithm/uSQXgsxu">k-way merge algorithm</a></li> <li>Simple merge algorithm</li> <li>Union (merge, with elements on the output not repeated)</li></ul> <h4>Sequence permutations</h4> <p class="note">Further information: <a href="/facts/Permutation/JSw9ukmv">Permutation</a></p> <ul><li><a href="/facts/Fisher%25E2%2580%2593Yates_shuffle/fIkuVG2X">Fisher–Yates shuffle</a> (also known as the Knuth shuffle): randomly shuffle a finite set</li> <li><a href="/facts/Heap%2527s_algorithm/mmlpjGYs">Heap's permutation generation algorithm</a>: interchange elements to generate next permutation</li> <li><a href="/facts/Schensted_algorithm/puYomvIg">Schensted algorithm</a>: constructs a pair of <a href="/facts/Young_tableau/e5lI4bck">Young tableaux</a> from a permutation</li> <li><a href="/facts/Steinhaus%25E2%2580%2593Johnson%25E2%2580%2593Trotter_algorithm/eIt7LXau">Steinhaus–Johnson–Trotter algorithm</a> (also known as the Johnson–Trotter algorithm): generates permutations by transposing elements</li></ul> <h4>Sequence combinations</h4> <p class="note">Further information: <a href="/facts/Combination/nmvrhMm1">Combination</a></p> <h4>Sequence alignment</h4> <ul><li><a href="/facts/Dynamic_time_warping/guEHSMw4">Dynamic time warping</a>: measure similarity between two sequences which may vary in time or speed</li> <li><a href="/facts/Hirschberg%2527s_algorithm/1CjG3ApW">Hirschberg's algorithm</a>: finds the least cost <a href="/facts/Sequence_alignment/p8GQfF7b">sequence alignment</a> between two sequences, as measured by their <a href="/facts/Levenshtein_distance/F0otyNSl">Levenshtein distance</a></li> <li><a href="/facts/Needleman%25E2%2580%2593Wunsch_algorithm/B3HJ8xU5">Needleman–Wunsch algorithm</a>: find global alignment between two sequences</li> <li><a href="/facts/Smith%25E2%2580%2593Waterman_algorithm/pvfmhpQB">Smith–Waterman algorithm</a>: find local sequence alignment</li></ul> <h4>Sequence sorting</h4> <p class="note">Main article: <a href="/facts/Sorting_algorithm/PwHpj1Gs">Sorting algorithm</a></p> <ul><li>Exchange sorts <ul><li><a href="/facts/Bubble_sort/Go9JnLk2">Bubble sort</a>: for each pair of indices, swap the items if out of order</li> <li><a href="/facts/Cocktail_shaker_sort/D8HBV8To">Cocktail shaker sort</a> or bidirectional bubble sort, a bubble sort traversing the list alternately from front to back and back to front</li> <li><a href="/facts/Comb_sort/kUpRPyBY">Comb sort</a></li> <li><a href="/facts/Gnome_sort/aXHk4XTv">Gnome sort</a></li> <li><a href="/facts/Odd%25E2%2580%2593even_sort/BjSCRzsb">Odd–even sort</a></li> <li><a href="/facts/Quicksort/1BeqhLAH">Quicksort</a>: divide list into two, with all items on the first list coming before all items on the second list.; then sort the two lists. Often the method of choice</li></ul></li> <li>Humorous or ineffective <ul><li><a href="/facts/Bogosort/bmg99Nz5">Bogosort</a>: the list is randomly shuffled until it happens to be sorted</li> <li><a href="/facts/Slowsort/Sa5Y0FGy">Slowsort</a></li> <li>Stalin sort: all elements that are not in order are removed from the list<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a></li> <li><a href="/facts/Stooge_sort/43XX0L6p">Stooge sort</a></li></ul></li> <li>Hybrid <ul><li><a href="/facts/Flashsort/U2LYor4S">Flashsort</a></li> <li><a href="/facts/Introsort/P9LHFUsD">Introsort</a>: begin with quicksort and switch to heapsort when the recursion depth exceeds a certain level</li> <li><a href="/facts/Timsort/llcssLEF">Timsort</a>: adaptative algorithm derived from merge sort and insertion sort. Used in Python 2.3 and up, and Java SE 7.</li></ul></li> <li>Insertion sorts <ul><li><a href="/facts/Cycle_sort/JWzhwyNP">Cycle sort</a>: in-place with theoretically optimal number of writes</li> <li><a href="/facts/Insertion_sort/N5yWe8Co">Insertion sort</a>: determine where the current item belongs in the list of sorted ones, and insert it there</li> <li><a href="/facts/Library_sort/fjShwFdS">Library sort</a></li> <li><a href="/facts/Patience_sorting/zNkBlmgM">Patience sorting</a></li> <li><a href="/facts/Shellsort/DH8sVBfj">Shell sort</a>: an attempt to improve insertion sort</li> <li><a href="/facts/Tree_sort/t3PnVBnK">Tree sort</a> (binary tree sort): build binary tree, then traverse it to create sorted list</li></ul></li> <li>Merge sorts <ul><li><a href="/facts/Merge_sort/A5jLYfzS">Merge sort</a>: sort the first and second half of the list separately, then merge the sorted lists</li> <li><a href="/facts/Slowsort/Sa5Y0FGy">Slowsort</a></li> <li><a href="/facts/Strand_sort/9h3JFjTI">Strand sort</a></li></ul></li> <li>Non-comparison sorts <ul><li><a href="/facts/Bead_sort/XjsxsakE">Bead sort</a></li> <li><a href="/facts/Bucket_sort/SuxxHqcc">Bucket sort</a></li> <li><a href="/facts/Burstsort/ETUxpf5K">Burstsort</a>: build a compact, cache efficient burst trie and then traverse it to create sorted output</li> <li><a href="/facts/Counting_sort/68vdcy9Y">Counting sort</a></li> <li><a href="/facts/Pigeonhole_sort/SaIEbEyV">Pigeonhole sort</a></li> <li><a href="/facts/Postman_sort/SuxxHqcc">Postman sort</a>: variant of Bucket sort which takes advantage of hierarchical structure</li> <li><a href="/facts/Radix_sort/ISe6XYJN">Radix sort</a>: sorts strings letter by letter</li></ul></li> <li>Selection sorts <ul><li><a href="/facts/Heapsort/Cz22lLKq">Heapsort</a>: convert the list into a heap, keep removing the largest element from the heap and adding it to the end of the list</li> <li><a href="/facts/Selection_sort/uIsGffcr">Selection sort</a>: pick the smallest of the remaining elements, add it to the end of the sorted list</li> <li><a href="/facts/Smoothsort/uUSa85ML">Smoothsort</a></li></ul></li> <li>Other <ul><li><a href="/facts/Bitonic_sorter/MdYdIbQV">Bitonic sorter</a></li> <li><a href="/facts/Pancake_sorting/tejLXXL6">Pancake sorting</a></li> <li><a href="/facts/Spaghetti_sort/UAxClDks">Spaghetti sort</a></li> <li><a href="/facts/Topological_sorting/VY7gNtYA">Topological sort</a></li></ul></li> <li>Unknown class <ul><li><a href="/facts/Samplesort/DwRbasbf">Samplesort</a></li></ul></li></ul> <h4>Subsequences</h4> <p class="note">Further information: <a href="/facts/Subsequence/GdC2Qwau">Subsequence</a></p> <ul><li><a href="/facts/Longest_common_subsequence_problem/2HKIa0yd">Longest common subsequence problem</a>: Find the longest subsequence common to all sequences in a set of sequences</li> <li><a href="/facts/Longest_increasing_subsequence_problem/vodfwHwH">Longest increasing subsequence problem</a>: Find the longest increasing subsequence of a given sequence</li> <li><a href="/facts/Ruzzo%25E2%2580%2593Tompa_algorithm/MPVEep7M">Ruzzo–Tompa algorithm</a>: Find all non-overlapping, contiguous, maximal scoring subsequences in a sequence of real numbers</li> <li><a href="/facts/Shortest_common_supersequence_problem/oR3PSgxW">Shortest common supersequence problem</a>: Find the shortest supersequence that contains two or more sequences as subsequences</li></ul> <h4>Substrings</h4> <p class="note">Further information: <a href="/facts/Substrings/dM5Rqg6X">Substrings</a></p> <ul><li><a href="/facts/Kadane%2527s_algorithm/bazjDTgq">Kadane's algorithm</a>: finds the contiguous subarray with largest sum in an array of numbers</li> <li><a href="/facts/Longest_common_substring_problem/hWmjK5xk">Longest common substring problem</a>: find the longest string (or strings) that is a substring (or are substrings) of two or more strings</li> <li><a href="/facts/Matching_wildcards/4MPh70p6">Matching wildcards</a> <ul><li><a href="/facts/Krauss_matching_wildcards_algorithm/xBFgmIgr">Krauss matching wildcards algorithm</a>: an open-source non-recursive algorithm</li> <li><a href="/facts/InterNetNews/LrKsDuvy">Rich Salz</a>' <a href="/facts/Wildmat/NEDqu4ER">wildmat</a>: a widely used <a href="/facts/Open-source_software/HzTaB8E9">open-source</a> <a href="/facts/Recursion/CxSKxJoW">recursive</a> algorithm</li></ul></li> <li><a href="/facts/Substring_search/RCvwDRle">Substring search</a> <ul><li><a href="/facts/Aho%25E2%2580%2593Corasick_string_matching_algorithm/huUFNcv8">Aho–Corasick string matching algorithm</a>: <a href="/facts/Trie/cXNr0ScT">trie</a> based algorithm for finding all substring matches to any of a finite set of strings</li> <li><a href="/facts/Boyer%25E2%2580%2593Moore%25E2%2580%2593Horspool_algorithm/rr8hEIIR">Boyer–Moore–Horspool algorithm</a>: Simplification of Boyer–Moore</li> <li><a href="/facts/Boyer%25E2%2580%2593Moore_string-search_algorithm/yUGSAvN6">Boyer–Moore string-search algorithm</a>: amortized linear (<a href="/facts/Sublinear/u1NglYpF">sublinear</a> in most times) algorithm for substring search</li> <li><a href="/facts/Knuth%25E2%2580%2593Morris%25E2%2580%2593Pratt_algorithm/A4uM3D8e">Knuth–Morris–Pratt algorithm</a>: substring search which bypasses reexamination of matched characters</li> <li><a href="/facts/Rabin%25E2%2580%2593Karp_string_search_algorithm/Wf7f0F53">Rabin–Karp string search algorithm</a>: searches multiple patterns efficiently</li> <li><a href="/facts/Zhu%25E2%2580%2593Takaoka_string_matching_algorithm/mBbLaV78">Zhu–Takaoka string matching algorithm</a>: a variant of Boyer–Moore</li></ul></li> <li><a href="/facts/Ukkonen%2527s_algorithm/JwdaVn8E">Ukkonen's algorithm</a>: a <a href="/facts/Linear-time/77T62gmf">linear-time</a>, <a href="/facts/Online_algorithm/64TsU7Yz">online algorithm</a> for constructing <a href="/facts/Suffix_tree/pdQdCxbe">suffix trees</a></li></ul> <h2 id="computational-mathematics">Computational mathematics</h2> <p class="note">Further information: <a href="/facts/Computational_mathematics/JRoX1lu0">Computational mathematics</a></p> <p class="note">See also: Combinatorial algorithms and Computational science</p> <h3>Abstract algebra</h3> <p class="note">Further information: <a href="/facts/Abstract_algebra/YNNE1CNz">Abstract algebra</a></p> <ul><li><a href="/facts/Chien_search/qfu4wEL6">Chien search</a>: a recursive algorithm for determining roots of polynomials defined over a finite field</li> <li><a href="/facts/Schreier%25E2%2580%2593Sims_algorithm/ugYjVQkM">Schreier–Sims algorithm</a>: computing a base and <a href="/facts/Strong_generating_set/09HzLIDL">strong generating set</a> (BSGS) of a <a href="/facts/Permutation_group/vRsNNwwx">permutation group</a></li> <li><a href="/facts/Todd%25E2%2580%2593Coxeter_algorithm/ekR0d3Rg">Todd–Coxeter algorithm</a>: Procedure for generating <a href="/facts/Coset/zFgQUTLY">cosets</a>.</li></ul> <h3>Computer algebra</h3> <p class="note">Further information: <a href="/facts/Computer_algebra/hjun1KAX">Computer algebra</a></p> <ul><li><a href="/facts/Buchberger%2527s_algorithm/7z5q4K33">Buchberger's algorithm</a>: finds a <a href="/facts/Gr%25C3%25B6bner_basis/efMrjM7w">Gröbner basis</a></li> <li><a href="/facts/Cantor%25E2%2580%2593Zassenhaus_algorithm/47YRHbun">Cantor–Zassenhaus algorithm</a>: factor polynomials over finite fields</li> <li><a href="/facts/Faug%25C3%25A8re_F4_algorithm/utY6u6tn">Faugère F4 algorithm</a>: finds a Gröbner basis (also mentions the F5 algorithm)</li> <li><a href="/facts/Gosper%2527s_algorithm/Iu7Jc8zQ">Gosper's algorithm</a>: find sums of hypergeometric terms that are themselves hypergeometric terms</li> <li><a href="/facts/Knuth%25E2%2580%2593Bendix_completion_algorithm/cH66W8Rr">Knuth–Bendix completion algorithm</a>: for <a href="/facts/Rewriting/9PHlnnnJ">rewriting</a> rule systems</li> <li><a href="/facts/Multivariate_division_algorithm/efMrjM7w">Multivariate division algorithm</a>: for <a href="/facts/Polynomial/Lzak8VVx">polynomials</a> in several indeterminates</li> <li><a href="/facts/Pollard%2527s_kangaroo_algorithm/qg3rvpY9">Pollard's kangaroo algorithm</a> (also known as Pollard's lambda algorithm): an algorithm for solving the discrete logarithm problem</li> <li><a href="/facts/Polynomial_long_division/MgJlJ2G7">Polynomial long division</a>: an algorithm for dividing a polynomial by another polynomial of the same or lower degree</li> <li><a href="/facts/Risch_algorithm/UcT2qrPl">Risch algorithm</a>: an algorithm for the calculus operation of indefinite integration (i.e. finding <a href="/facts/Antiderivatives/5qDsudIv">antiderivatives</a>)</li></ul> <h3>Geometry</h3> <p class="note">Main category: Geometric algorithms</p> <p class="note">Further information: <a href="/facts/Computational_geometry/eeaotQtl">Computational geometry</a></p> <ul><li><a href="/facts/Closest_pair_problem/54Aw1kRV">Closest pair problem</a>: find the pair of points (from a set of points) with the smallest distance between them</li> <li><a href="/facts/Collision_detection/kXkE9WXv">Collision detection</a> algorithms: check for the collision or intersection of two given solids</li> <li><a href="/facts/Cone_algorithm/c2fSavqY">Cone algorithm</a>: identify surface points</li> <li><a href="/facts/Convex_hull_algorithms/Wr70A2AI">Convex hull algorithms</a>: determining the <a href="/facts/Convex_hull/D4Id3JDS">convex hull</a> of a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> of points <ul><li><a href="/facts/Chan%2527s_algorithm/DyCgtttL">Chan's algorithm</a></li> <li><a href="/facts/Gift_wrapping_algorithm/4V8z8eHC">Gift wrapping algorithm</a> or Jarvis march</li> <li><a href="/facts/Graham_scan/WmFuJzEg">Graham scan</a></li> <li><a href="/facts/Kirkpatrick%25E2%2580%2593Seidel_algorithm/h2E4vCMN">Kirkpatrick–Seidel algorithm</a></li> <li><a href="/facts/Quickhull/XEeXGNNr">Quickhull</a></li></ul></li> <li><a href="/facts/Euclidean_distance_map/IeAfIYua">Euclidean distance transform</a>: computes the distance between every point in a grid and a discrete collection of points.</li> <li><a href="/facts/Geometric_hashing/DPl2SNWx">Geometric hashing</a>: a method for efficiently finding two-dimensional objects represented by discrete points that have undergone an <a href="/facts/Affine_transformation/BD7yDr10">affine transformation</a></li> <li><a href="/facts/Gilbert%25E2%2580%2593Johnson%25E2%2580%2593Keerthi_distance_algorithm/jpAx0cVh">Gilbert–Johnson–Keerthi distance algorithm</a>: determining the smallest distance between two <a href="/facts/Convex_set/vdAuJRJl">convex</a> shapes.</li> <li><a href="/facts/Jump-and-Walk_algorithm/fC1Vapjz">Jump-and-Walk algorithm</a>: an algorithm for point location in triangulations</li> <li><a href="/facts/Laplacian_smoothing/jWSt85SJ">Laplacian smoothing</a>: an algorithm to smooth a polygonal mesh</li> <li><a href="/facts/Line_segment_intersection/RwH57yPq">Line segment intersection</a>: finding whether lines intersect, usually with a <a href="/facts/Sweep_line_algorithm/phUJCw6U">sweep line algorithm</a> <ul><li><a href="/facts/Bentley%25E2%2580%2593Ottmann_algorithm/djAFj5I5">Bentley–Ottmann algorithm</a></li> <li>Shamos–Hoey algorithm</li></ul></li> <li><a href="/facts/Minimum_bounding_box_algorithms/NgMKHabc">Minimum bounding box algorithms</a>: find the <a href="/facts/Minimum_bounding_box/oFHL8bxI">oriented minimum bounding box</a> enclosing a set of points</li> <li><a href="/facts/Nearest_neighbor_search/R6QTyAph">Nearest neighbor search</a>: find the nearest point or points to a query point</li> <li><a href="/facts/Nesting_algorithm/aHv1UsyX">Nesting algorithm</a>: make the most efficient use of material or space</li> <li><a href="/facts/Point_in_polygon/acr2LQ1n">Point in polygon</a> algorithms: tests whether a given point lies within a given polygon</li> <li><a href="/facts/Point_set_registration/EevAmm50">Point set registration</a> algorithms: finds the transformation between two <a href="/facts/Point_cloud/dN8eG4AU">point sets</a> to optimally align them.</li> <li><a href="/facts/Rotating_calipers/SkbtSxWV">Rotating calipers</a>: determine all <a href="/facts/Antipodal_point/2V3228jA">antipodal</a> pairs of points and vertices on a <a href="/facts/Convex_polygon/7x35w610">convex polygon</a> or <a href="/facts/Convex_hull/D4Id3JDS">convex hull</a>.</li> <li><a href="/facts/Shoelace_algorithm/7RJepeLh">Shoelace algorithm</a>: determine the area of a polygon whose vertices are described by ordered pairs in the plane</li> <li><a href="/facts/Triangulation_(geometry)/enYNhLNy">Triangulation</a> <ul><li><a href="/facts/Delaunay_triangulation/6VRk7cS9">Delaunay triangulation</a> <ul><li><a href="/facts/Chew%2527s_second_algorithm/ybkVxs4n">Chew's second algorithm</a>: create quality <a href="/facts/Constrained_Delaunay_triangulation/mbveVl5v">constrained Delaunay triangulations</a></li> <li><a href="/facts/Ruppert%2527s_algorithm/ybkVxs4n">Ruppert's algorithm</a> (also known as Delaunay refinement): create quality Delaunay triangulations</li></ul></li> <li><a href="/facts/Marching_triangles/ap2Yg5FJ">Marching triangles</a>: reconstruct two-dimensional surface geometry from an unstructured <a href="/facts/Point_cloud/dN8eG4AU">point cloud</a></li> <li><a href="/facts/Polygon_triangulation/FF0205ye">Polygon triangulation</a> algorithms: decompose a polygon into a set of triangles</li> <li><a href="/facts/Quasitriangulation/7dmYBHUW">Quasitriangulation</a></li> <li><a href="/facts/Voronoi_diagram/AhQY5LD8">Voronoi diagrams</a>, geometric <a href="/facts/Duality_(mathematics)/8jGuyQIU">dual</a> of <a href="/facts/Delaunay_triangulation/6VRk7cS9">Delaunay triangulation</a> <ul><li><a href="/facts/Bowyer%25E2%2580%2593Watson_algorithm/q0LNteIc">Bowyer–Watson algorithm</a>: create voronoi diagram in any number of dimensions</li> <li><a href="/facts/Fortune%2527s_Algorithm/FDUyGGDJ">Fortune's Algorithm</a>: create voronoi diagram</li></ul></li></ul></li></ul> <h3>Number theoretic algorithms</h3> <p class="note">Further information: <a href="/facts/Number_theory/zhoa7zrc">Number theory</a></p> <ul><li><a href="/facts/Binary_GCD_algorithm/AS9LC3NQ">Binary GCD algorithm</a>: Efficient way of calculating GCD.</li> <li><a href="/facts/Booth%2527s_multiplication_algorithm/CplEqXtt">Booth's multiplication algorithm</a></li> <li><a href="/facts/Chakravala_method/aEsVHc7s">Chakravala method</a>: a cyclic algorithm to solve indeterminate quadratic equations, including <a href="/facts/Pell%2527s_equation/n0ul61eQ">Pell's equation</a></li> <li><a href="/facts/Discrete_logarithm/k8TXh5bL">Discrete logarithm</a>: <ul><li><a href="/facts/Baby-step_giant-step/AWR8opeS">Baby-step giant-step</a></li> <li><a href="/facts/Index_calculus_algorithm/peE7HdUT">Index calculus algorithm</a></li> <li><a href="/facts/Pohlig%25E2%2580%2593Hellman_algorithm/f6jBHbbS">Pohlig–Hellman algorithm</a></li> <li><a href="/facts/Pollard%2527s_rho_algorithm_for_logarithms/UFayJQrH">Pollard's rho algorithm for logarithms</a></li></ul></li> <li><a href="/facts/Euclidean_algorithm/wApql29c">Euclidean algorithm</a>: computes the <a href="/facts/Greatest_common_divisor/kNFvBuKl">greatest common divisor</a></li> <li><a href="/facts/Extended_Euclidean_algorithm/wmomforl">Extended Euclidean algorithm</a>: also solves the equation <i>ax</i> + <i>by</i> = <i>c</i></li> <li><a href="/facts/Integer_factorization/EjMCTz2t">Integer factorization</a>: breaking an integer into its <a href="/facts/Prime_number/L20FLkgn">prime</a> factors <ul><li><a href="/facts/Congruence_of_squares/1MFSr2Dx">Congruence of squares</a></li> <li><a href="/facts/Dixon%2527s_algorithm/Qqp6eMx4">Dixon's algorithm</a></li> <li><a href="/facts/Fermat%2527s_factorization_method/XecvbCoo">Fermat's factorization method</a></li> <li><a href="/facts/General_number_field_sieve/elC06ARC">General number field sieve</a></li> <li><a href="/facts/Lenstra_elliptic_curve_factorization/PwdIdtQW">Lenstra elliptic curve factorization</a></li> <li><a href="/facts/Pollard%2527s_p_%25E2%2588%2592_1_algorithm/dITySRp5">Pollard's <i>p</i> − 1 algorithm</a></li> <li><a href="/facts/Pollard%2527s_rho_algorithm/7TjSCKK5">Pollard's rho algorithm</a></li> <li><a href="/facts/Prime_factorization_algorithm/EjMCTz2t">prime factorization algorithm</a></li> <li><a href="/facts/Quadratic_sieve/xDrfU9xl">Quadratic sieve</a></li> <li><a href="/facts/Shor%2527s_algorithm/9JwEtznC">Shor's algorithm</a></li> <li><a href="/facts/Special_number_field_sieve/vnlM5Tb7">Special number field sieve</a></li> <li><a href="/facts/Trial_division/YwFdWcWb">Trial division</a></li></ul></li> <li><a href="/facts/Lenstra%25E2%2580%2593Lenstra%25E2%2580%2593Lov%25C3%25A1sz_lattice_basis_reduction_algorithm/hadYSXGw">Lenstra–Lenstra–Lovász algorithm</a> (also known as LLL algorithm): find a short, nearly orthogonal <a href="/facts/Lattice_(group)/2ls9Iv9N">lattice</a> <a href="/facts/Basis_(linear_algebra)/89IPoN6c">basis</a> in polynomial time</li> <li><a href="/facts/Modular_square_root/rHD2uQdQ">Modular square root</a>: computing square roots modulo a prime number <ul><li><a href="/facts/Berlekamp%2527s_root_finding_algorithm/dNuGwhYn">Berlekamp's root finding algorithm</a></li> <li><a href="/facts/Cipolla%2527s_algorithm/mfcWWvE8">Cipolla's algorithm</a></li> <li><a href="/facts/Tonelli%25E2%2580%2593Shanks_algorithm/tdxF6hfd">Tonelli–Shanks algorithm</a></li></ul></li> <li><a href="/facts/Multiplication_algorithm/68xf6EdK">Multiplication algorithms</a>: fast multiplication of two numbers <ul><li><a href="/facts/Karatsuba_algorithm/YFk3dnqX">Karatsuba algorithm</a></li> <li><a href="/facts/Sch%25C3%25B6nhage%25E2%2580%2593Strassen_algorithm/7dLGaI4d">Schönhage–Strassen algorithm</a></li> <li><a href="/facts/Toom%25E2%2580%2593Cook_multiplication/5AuKo2IJ">Toom–Cook multiplication</a></li></ul></li> <li><a href="/facts/Odlyzko%25E2%2580%2593Sch%25C3%25B6nhage_algorithm/rUNLSzJm">Odlyzko–Schönhage algorithm</a>: calculates nontrivial zeroes of the <a href="/facts/Riemann_zeta_function/MnfRu7lY">Riemann zeta function</a></li> <li><a href="/facts/Primality_test/dLMr8E0u">Primality tests</a>: determining whether a given number is <a href="/facts/Prime_number/L20FLkgn">prime</a> <ul><li><a href="/facts/AKS_primality_test/VRkvQVeT">AKS primality test</a></li> <li><a href="/facts/Baillie%25E2%2580%2593PSW_primality_test/y2FlVSfx">Baillie–PSW primality test</a></li> <li><a href="/facts/Fermat_primality_test/4weCrWtE">Fermat primality test</a></li> <li><a href="/facts/Lucas_primality_test/Dxq6trsK">Lucas primality test</a></li> <li><a href="/facts/Miller%25E2%2580%2593Rabin_primality_test/FWx93kWC">Miller–Rabin primality test</a></li> <li><a href="/facts/Sieve_of_Atkin/dl629eAx">Sieve of Atkin</a></li> <li><a href="/facts/Sieve_of_Eratosthenes/ACzqmLGE">Sieve of Eratosthenes</a></li> <li><a href="/facts/Sieve_of_Sundaram/uPM8gAd6">Sieve of Sundaram</a></li></ul></li></ul> <h3>Numerical algorithms</h3> <p class="note">Further information: <a href="/facts/List_of_numerical_analysis_topics/YlB1g58n">List of numerical analysis topics</a> and <a href="/facts/Numerical_analysis/QT9cYa9z">Numerical analysis</a></p> <h4>Differential equation solving</h4> <p class="note">Further information: <a href="/facts/Differential_equation/9MGbE3Ca">Differential equation</a></p> <ul><li><a href="/facts/Backward_Euler_method/lccBRRYY">Backward Euler method</a></li> <li><a href="/facts/Euler_method/7yF5B4z9">Euler method</a></li> <li><a href="/facts/Linear_multistep_method/Q1taSMtG">Linear multistep methods</a></li> <li><a href="/facts/Multigrid_method/6FTEwkja">Multigrid methods</a> (MG methods), a group of algorithms for solving differential equations using a hierarchy of discretizations</li> <li><a href="/facts/Partial_differential_equation/DyPsBlv7">Partial differential equation</a>: <ul><li><a href="/facts/Crank%25E2%2580%2593Nicolson_method/6RnaoWIP">Crank–Nicolson method</a> for diffusion equations</li> <li><a href="/facts/Finite_difference_method/EoG81Qn9">Finite difference method</a></li> <li><a href="/facts/Lax%25E2%2580%2593Wendroff_method/MjBjI50f">Lax–Wendroff</a> for wave equations</li></ul></li> <li><a href="/facts/Runge%25E2%2580%2593Kutta_methods/YRjbyHpY">Runge–Kutta methods</a> <ul><li><a href="/facts/Euler_integration/7yF5B4z9">Euler integration</a></li></ul></li> <li><a href="/facts/Trapezoidal_rule_(differential_equations)/vlUlTgYv">Trapezoidal rule (differential equations)</a></li> <li><a href="/facts/Verlet_integration/Wtzt8hkX">Verlet integration</a> (French pronunciation: [vɛʁˈlɛ]): integrate Newton's equations of motion</li></ul> <h4>Elementary and special functions</h4> <p class="note">Further information: <a href="/facts/Special_functions/JETSeucA">Special functions</a></p> <ul><li><a href="/facts/Computing_%25CF%2580/03SQhgcM">Computation of π</a>: <ul><li><a href="/facts/Bailey%25E2%2580%2593Borwein%25E2%2580%2593Plouffe_formula/m4v34n9d">Bailey–Borwein–Plouffe formula</a>: (BBP formula) a spigot algorithm for the computation of the nth binary digit of π</li> <li><a href="/facts/Borwein%2527s_algorithm/MpPBybAo">Borwein's algorithm</a>: an algorithm to calculate the value of 1/π</li> <li><a href="/facts/Chudnovsky_algorithm/cQmCNhEn">Chudnovsky algorithm</a>: a fast method for calculating the digits of π</li> <li><a href="/facts/Gauss%25E2%2580%2593Legendre_algorithm/QqzIk2L6">Gauss–Legendre algorithm</a>: computes the digits of <a href="/facts/Pi/vC0UBj1q">pi</a></li></ul></li> <li><a href="/facts/Division_algorithm/8xc3I1sJ">Division algorithms</a>: for computing quotient and/or remainder of two numbers <ul><li><a href="/facts/Goldschmidt_division/8xc3I1sJ">Goldschmidt division</a></li> <li><a href="/facts/Long_division/W8Vd90Kw">Long division</a></li> <li><a href="/facts/Newton%25E2%2580%2593Raphson_division/8xc3I1sJ">Newton–Raphson division</a>: uses <a href="/facts/Newton%2527s_method/VlRhI2FL">Newton's method</a> to find the <a href="/facts/Multiplicative_inverse/yczdYyCw">reciprocal</a> of D, and multiply that reciprocal by N to find the final quotient Q.</li> <li><a href="/facts/Non-restoring_division/8xc3I1sJ">Non-restoring division</a></li> <li><a href="/facts/Restoring_division/8xc3I1sJ">Restoring division</a></li> <li><a href="/facts/SRT_division/8xc3I1sJ">SRT division</a></li></ul></li> <li>Exponentiation: <ul><li><a href="/facts/Addition-chain_exponentiation/JkGjVadw">Addition-chain exponentiation</a>: exponentiation by positive integer powers that requires a minimal number of multiplications</li> <li><a href="/facts/Exponentiating_by_squaring/HP8H37AA">Exponentiating by squaring</a>: an algorithm used for the fast computation of <a href="/facts/Arbitrary-precision_arithmetic/cXxc8yB2">large integer</a> powers of a number</li></ul></li> <li>Hyperbolic and Trigonometric Functions: <ul><li><a href="/facts/BKM_algorithm/e0r1Wszn">BKM algorithm</a>: computes <a href="/facts/Elementary_function_(differential_algebra)/wVFyDwu8">elementary functions</a> using a table of logarithms</li> <li><a href="/facts/CORDIC/sQqTjkd2">CORDIC</a>: computes hyperbolic and trigonometric functions using a table of arctangents</li></ul></li> <li><a href="/facts/Montgomery_reduction/C1UyVrKJ">Montgomery reduction</a>: an algorithm that allows <a href="/facts/Modular_arithmetic/0wtRa5dU">modular arithmetic</a> to be performed efficiently when the modulus is large</li> <li><a href="/facts/Multiplication_algorithm/68xf6EdK">Multiplication algorithms</a>: fast multiplication of two numbers <ul><li><a href="/facts/Booth%2527s_multiplication_algorithm/CplEqXtt">Booth's multiplication algorithm</a>: a multiplication algorithm that multiplies two signed binary numbers in two's complement notation</li> <li><a href="/facts/F%25C3%25BCrer%2527s_algorithm/yz1YBWct">Fürer's algorithm</a>: an integer multiplication algorithm for very large numbers possessing a very low <a href="/facts/Computational_complexity_theory/etHuVF3U">asymptotic complexity</a></li> <li><a href="/facts/Karatsuba_algorithm/YFk3dnqX">Karatsuba algorithm</a>: an efficient procedure for multiplying large numbers</li> <li><a href="/facts/Sch%25C3%25B6nhage%25E2%2580%2593Strassen_algorithm/7dLGaI4d">Schönhage–Strassen algorithm</a>: an asymptotically fast multiplication algorithm for large integers</li> <li><a href="/facts/Toom%25E2%2580%2593Cook_multiplication/5AuKo2IJ">Toom–Cook multiplication</a>: (Toom3) a multiplication algorithm for large integers</li></ul></li> <li><a href="/facts/Multiplicative_inverse/yczdYyCw">Multiplicative inverse Algorithms</a>: for computing a number's multiplicative inverse (reciprocal). <ul><li><a href="/facts/Newton%2527s_method/VlRhI2FL">Newton's method</a></li></ul></li> <li><a href="/facts/Rounding_functions/rCLYXN00">Rounding functions</a>: the classic ways to round numbers</li> <li><a href="/facts/Spigot_algorithm/erV8opXS">Spigot algorithm</a>: a way to compute the value of a <a href="/facts/Mathematical_constant/rzqTX307">mathematical constant</a> without knowing preceding digits</li> <li>Square and Nth root of a number: <ul><li><a href="/facts/Alpha_max_plus_beta_min_algorithm/0aBKezrL">Alpha max plus beta min algorithm</a>: an approximation of the square-root of the sum of two squares</li> <li><a href="/facts/Methods_of_computing_square_roots/dRG2BtBp">Methods of computing square roots</a></li> <li><a href="/facts/Nth_root_algorithm/XrRjtJGe"><i>n</i>th root algorithm</a></li></ul></li> <li>Summation: <ul><li><a href="/facts/Binary_splitting/yVk20XmE">Binary splitting</a>: a <a href="/facts/Divide_and_conquer_algorithm/pC1X7Ws7">divide and conquer</a> technique which speeds up the numerical evaluation of many types of series with rational terms</li> <li><a href="/facts/Kahan_summation_algorithm/6a3meV1l">Kahan summation algorithm</a>: a more accurate method of summing floating-point numbers</li></ul></li> <li><a href="/facts/Unrestricted_algorithm/mys8S4GE">Unrestricted algorithm</a></li></ul> <h4>Geometric</h4> <ul><li><a href="/facts/Radon_transform/JskFJRMS">Filtered back-projection</a>: efficiently computes the inverse 2-dimensional <a href="/facts/Radon_transform/JskFJRMS">Radon transform</a>.</li> <li><a href="/facts/Level_set_method/jTDtmENI">Level set method</a> (LSM): a numerical technique for tracking interfaces and shapes</li></ul> <h4>Interpolation and extrapolation</h4> <p class="note">Further information: <a href="/facts/Extrapolation/wggUrqjF">Extrapolation</a> and <a href="/facts/Interpolation/8PyetX4f">Interpolation</a></p> <ul><li><a href="/facts/Birkhoff_interpolation/vAW9NlC2">Birkhoff interpolation</a>: an extension of polynomial interpolation</li> <li><a href="/facts/Cubic_interpolation/S29nwRUF">Cubic interpolation</a></li> <li><a href="/facts/Hermite_interpolation/u36d6yH2">Hermite interpolation</a></li> <li><a href="/facts/Lagrange_interpolation/MnpMmhtC">Lagrange interpolation</a>: interpolation using <a href="/facts/Lagrange_polynomial/MnpMmhtC">Lagrange polynomials</a></li> <li><a href="/facts/Linear_interpolation/galkvRGy">Linear interpolation</a>: a method of curve fitting using linear polynomials</li> <li><a href="/facts/Monotone_cubic_interpolation/3LlrJ032">Monotone cubic interpolation</a>: a variant of cubic interpolation that preserves monotonicity of the data set being interpolated.</li> <li><a href="/facts/Multivariate_interpolation/qj0F4Jze">Multivariate interpolation</a> <ul><li><a href="/facts/Bicubic_interpolation/Fov96ol8">Bicubic interpolation</a>: a generalization of <a href="/facts/Cubic_interpolation/S29nwRUF">cubic interpolation</a> to two dimensions</li> <li><a href="/facts/Bilinear_interpolation/yoke6SzF">Bilinear interpolation</a>: an extension of <a href="/facts/Linear_interpolation/galkvRGy">linear interpolation</a> for interpolating functions of two variables on a regular grid</li> <li><a href="/facts/Lanczos_resampling/uup50eym">Lanczos resampling</a> ("Lanzosh"): a multivariate interpolation method used to compute new values for any digitally sampled data</li> <li><a href="/facts/Nearest-neighbor_interpolation/AGHTPfEu">Nearest-neighbor interpolation</a></li> <li><a href="/facts/Tricubic_interpolation/U8EwEvLl">Tricubic interpolation</a>: a generalization of <a href="/facts/Cubic_interpolation/S29nwRUF">cubic interpolation</a> to three dimensions</li></ul></li> <li><a href="/facts/Pareto_interpolation/fCImXemW">Pareto interpolation</a>: a method of estimating the median and other properties of a population that follows a <a href="/facts/Pareto_distribution/PgMDbLrR">Pareto distribution</a>.</li> <li><a href="/facts/Polynomial_interpolation/DmnuxaKT">Polynomial interpolation</a> <ul><li><a href="/facts/Neville%2527s_algorithm/gSU1oeJs">Neville's algorithm</a></li></ul></li> <li><a href="/facts/Spline_interpolation/AowdpQwm">Spline interpolation</a>: Reduces error with <a href="/facts/Runge%2527s_phenomenon/641beUAR">Runge's phenomenon</a>. <ul><li><a href="/facts/De_Boor_algorithm/JUWNeY7n">De Boor algorithm</a>: <a href="/facts/B-spline/MLTCWCEd">B-splines</a></li> <li><a href="/facts/De_Casteljau%2527s_algorithm/UvCp8lwp">De Casteljau's algorithm</a>: <a href="/facts/B%25C3%25A9zier_curve/zJx3Uj60">Bézier curves</a></li></ul></li> <li><a href="/facts/Trigonometric_interpolation/CBpDzKwL">Trigonometric interpolation</a></li></ul> <h4>Linear algebra</h4> <p class="note">Further information: <a href="/facts/Numerical_linear_algebra/jnS6Tteb">Numerical linear algebra</a></p> <ul><li><a href="/facts/Eigenvalue_algorithm/AYecadB0">Eigenvalue algorithms</a> <ul><li><a href="/facts/Arnoldi_iteration/7bnLdCgy">Arnoldi iteration</a></li> <li><a href="/facts/Inverse_iteration/vvjavcom">Inverse iteration</a></li> <li><a href="/facts/Jacobi_eigenvalue_algorithm/0gE5vpje">Jacobi method</a></li> <li><a href="/facts/Lanczos_iteration/t3n5RYKr">Lanczos iteration</a></li> <li><a href="/facts/Power_iteration/gLwIJmjV">Power iteration</a></li> <li><a href="/facts/QR_algorithm/7LfgtT40">QR algorithm</a></li> <li><a href="/facts/Rayleigh_quotient_iteration/lj5UesPT">Rayleigh quotient iteration</a></li></ul></li> <li><a href="/facts/Gram%25E2%2580%2593Schmidt_process/vRNpld3t">Gram–Schmidt process</a>: orthogonalizes a set of vectors</li> <li>Krylov methods (for large sparse matrix problems; third most-important numerical method class of the 20th century as ranked by SISC; after fast-fourier and fast-multipole)</li> <li><a href="/facts/Matrix_multiplication_algorithm/VrYWxfDt">Matrix multiplication algorithms</a> <ul><li><a href="/facts/Cannon%2527s_algorithm/DpcEw4ta">Cannon's algorithm</a>: a <a href="/facts/Distributed_algorithm/S35ydYjK">distributed algorithm</a> for <a href="/facts/Matrix_multiplication/lYDB6Ro2">matrix multiplication</a> especially suitable for computers laid out in an N × N mesh</li> <li><a href="/facts/Coppersmith%25E2%2580%2593Winograd_algorithm/KCn5KUzd">Coppersmith–Winograd algorithm</a>: square <a href="/facts/Matrix_multiplication/lYDB6Ro2">matrix multiplication</a></li> <li><a href="/facts/Freivalds%2527_algorithm/wClqXGFR">Freivalds' algorithm</a>: a randomized algorithm used to verify matrix multiplication</li> <li><a href="/facts/Strassen_algorithm/rrIGRSNp">Strassen algorithm</a>: faster <a href="/facts/Matrix_multiplication/lYDB6Ro2">matrix multiplication</a></li></ul></li></ul> <ul><li>Solving <a href="/facts/System_of_linear_equations/fk9CFdgp">systems of linear equations</a> <ul><li><a href="/facts/Biconjugate_gradient_method/m1n1pSla">Biconjugate gradient method</a>: solves systems of linear equations</li> <li><a href="/facts/Conjugate_gradient/AFwzBS4U">Conjugate gradient</a>: an algorithm for the numerical solution of particular systems of linear equations</li> <li><a href="/facts/Gauss%25E2%2580%2593Jordan_elimination/23Rvf4ht">Gauss–Jordan elimination</a>: solves systems of linear equations</li> <li><a href="/facts/Gauss%25E2%2580%2593Seidel_method/eK94QeFt">Gauss–Seidel method</a>: solves systems of linear equations iteratively</li> <li><a href="/facts/Gaussian_elimination/23Rvf4ht">Gaussian elimination</a></li> <li><a href="/facts/Levinson_recursion/QwEFDA6a">Levinson recursion</a>: solves equation involving a <a href="/facts/Toeplitz_matrix/WAjSdlaW">Toeplitz matrix</a></li> <li><a href="/facts/Stone%2527s_method/2IakVyWI">Stone's method</a>: also known as the strongly implicit procedure or SIP, is an algorithm for solving a sparse linear system of equations</li> <li><a href="/facts/Successive_over-relaxation/rCUV11er">Successive over-relaxation</a> (SOR): method used to speed up convergence of the <a href="/facts/Gauss%25E2%2580%2593Seidel_method/eK94QeFt">Gauss–Seidel method</a></li> <li><a href="/facts/Tridiagonal_matrix_algorithm/NREF5x1c">Tridiagonal matrix algorithm</a> (Thomas algorithm): solves systems of tridiagonal equations</li></ul></li> <li><a href="/facts/Sparse_matrix/FFtN0XjR">Sparse matrix</a> algorithms <ul><li><a href="/facts/Cuthill%25E2%2580%2593McKee_algorithm/ab5ekCXk">Cuthill–McKee algorithm</a>: reduce the <a href="/facts/Bandwidth_(matrix_theory)/Iz803N35">bandwidth</a> of a <a href="/facts/Symmetric_sparse_matrix/FFtN0XjR">symmetric sparse matrix</a></li> <li><a href="/facts/Minimum_degree_algorithm/Mz1amAVQ">Minimum degree algorithm</a>: permute the rows and columns of a <a href="/facts/Symmetric_sparse_matrix/FFtN0XjR">symmetric sparse matrix</a> before applying the <a href="/facts/Cholesky_decomposition/Q3IjkuTs">Cholesky decomposition</a></li> <li><a href="/facts/Symbolic_Cholesky_decomposition/LJWKlXTy">Symbolic Cholesky decomposition</a>: Efficient way of storing <a href="/facts/Sparse_matrix/FFtN0XjR">sparse matrix</a></li></ul></li></ul> <h4>Monte Carlo</h4> <p class="note">Further information: <a href="/facts/Monte_Carlo_method/AkHjY7jc">Monte Carlo method</a></p> <ul><li><a href="/facts/Gibbs_sampling/HDYRhxEq">Gibbs sampling</a>: generates a sequence of samples from the joint probability distribution of two or more random variables</li> <li><a href="/facts/Hybrid_Monte_Carlo/CjkFLKFx">Hybrid Monte Carlo</a>: generates a sequence of samples using <a href="/facts/Hamiltonian_dynamics/2ReerlNA">Hamiltonian</a> weighted <a href="/facts/Markov_chain_Monte_Carlo/eTjk3WQy">Markov chain Monte Carlo</a>, from a probability distribution which is difficult to sample directly.</li> <li><a href="/facts/Metropolis%25E2%2580%2593Hastings_algorithm/8K7bz3LN">Metropolis–Hastings algorithm</a>: used to generate a sequence of samples from the <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> of one or more variables</li> <li><a href="/facts/Wang_and_Landau_algorithm/QfXQn5HN">Wang and Landau algorithm</a>: an extension of <a href="/facts/Metropolis%25E2%2580%2593Hastings_algorithm/8K7bz3LN">Metropolis–Hastings algorithm</a> sampling</li></ul> <h4>Numerical integration</h4> <p class="note">Further information: <a href="/facts/Numerical_integration/MwJnvcDV">Numerical integration</a></p> <ul><li><a href="/facts/MISER_algorithm/YefNEuUg">MISER algorithm</a>: Monte Carlo simulation, <a href="/facts/Numerical_integration/MwJnvcDV">numerical integration</a></li></ul> <h4>Root finding</h4> <p class="note">Main article: <a href="/facts/Root-finding_algorithm/IxTDkhBq">Root-finding algorithm</a></p> <ul><li><a href="/facts/Bisection_method/3tWmtoIp">Bisection method</a></li> <li><a href="/facts/False_position_method/bMuhM6pl">False position method</a>: and Illinois method: 2-point, bracketing</li> <li><a href="/facts/Halley%2527s_method/t0tcGcHA">Halley's method</a>: uses first and second derivatives</li> <li><a href="/facts/ITP_Method/tPzXpXEA">ITP method</a>: minmax optimal and superlinear convergence simultaneously</li> <li><a href="/facts/Muller%2527s_method/ouMwYWnz">Muller's method</a>: 3-point, quadratic interpolation</li> <li><a href="/facts/Newton%2527s_method/VlRhI2FL">Newton's method</a>: finds zeros of functions with <a href="/facts/Calculus/MEmUTYoz">calculus</a></li> <li><a href="/facts/Ridder%2527s_method/4wgrjMwn">Ridder's method</a>: 3-point, exponential scaling</li> <li><a href="/facts/Secant_method/tkNV8Rzk">Secant method</a>: 2-point, 1-sided</li></ul> <h3>Optimization algorithms</h3> <p class="note">Main article: <a href="/facts/Mathematical_optimization/oRn8Iv5I">Mathematical optimization</a></p><p><a href="/facts/Hybrid_algorithm/mgL7jc0c">Hybrid</a> Algorithms </p><ul><li><a href="/facts/Alpha%25E2%2580%2593beta_pruning/TRI5u3GL">Alpha–beta pruning</a>: search to reduce number of nodes in minimax algorithm</li> <li>A hybrid BFGS-Like method (see more <a href="https://doi.org/10.1016/j.cam.2024.115857">https://doi.org/10.1016/j.cam.2024.115857</a>)</li> <li><a href="/facts/Branch_and_bound/mhALtav7">Branch and bound</a></li> <li><a href="/facts/Bruss_algorithm/7aAph2N6">Bruss algorithm</a>: see <a href="/facts/Odds_algorithm/7aAph2N6">odds algorithm</a></li> <li><a href="/facts/Chain_matrix_multiplication/PMh2gS83">Chain matrix multiplication</a></li> <li><a href="/facts/Combinatorial_optimization/PTcloS79">Combinatorial optimization</a>: optimization problems where the set of feasible solutions is discrete <ul><li><a href="/facts/Greedy_randomized_adaptive_search_procedure/MYothUQN">Greedy randomized adaptive search procedure</a> (GRASP): successive constructions of a greedy randomized solution and subsequent iterative improvements of it through a local search</li> <li><a href="/facts/Hungarian_method/rRCJebc1">Hungarian method</a>: a combinatorial optimization algorithm which solves the <a href="/facts/Assignment_problem/dIMpM0aW">assignment problem</a> in polynomial time</li></ul></li> <li><a href="/facts/Conjugate_gradient_method/AFwzBS4U">Conjugate gradient methods</a> (see more <a href="https://doi.org/10.1016/j.jksus.2022.101923">https://doi.org/10.1016/j.jksus.2022.101923</a>)</li> <li><a href="/facts/Constraint_satisfaction/PXI74p1T">Constraint satisfaction</a> <ul><li><a href="/facts/AC-3_algorithm/LjoRWxd9">AC-3 algorithm</a> general algorithms for the constraint satisfaction</li> <li><a href="/facts/Chaff_algorithm/guPVSJ08">Chaff algorithm</a>: an algorithm for solving instances of the <a href="/facts/Boolean_satisfiability_problem/wBVRjWoy">Boolean satisfiability problem</a></li> <li><a href="/facts/Davis%25E2%2580%2593Putnam_algorithm/EowmALMU">Davis–Putnam algorithm</a>: check the validity of a first-order logic formula</li> <li><a href="/facts/Difference_map_algorithm/nkhgPmWU">Difference map algorithm</a> general algorithms for the constraint satisfaction</li> <li><a href="/facts/DPLL_algorithm/T3Tu45j3">Davis–Putnam–Logemann–Loveland algorithm</a> (DPLL): an algorithm for deciding the satisfiability of propositional logic formula in <a href="/facts/Conjunctive_normal_form/B3sY1lTW">conjunctive normal form</a>, i.e. for solving the <a href="/facts/CNF-SAT/wBVRjWoy">CNF-SAT</a> problem</li> <li><a href="/facts/Exact_cover/C7QcbDcN">Exact cover</a> problem</li> <li><a href="/facts/Min_conflicts_algorithm/X8jsbDCX">Min conflicts algorithm</a> general algorithms for the constraint satisfaction <ul><li><a href="/facts/Algorithm_X/bWDAEgKj">Algorithm X</a>: a <a href="/facts/Nondeterministic_algorithm/UubLdp3D">nondeterministic algorithm</a></li> <li><a href="/facts/Dancing_Links/WpaSJyuV">Dancing Links</a>: an efficient implementation of Algorithm X</li></ul></li></ul></li> <li><a href="/facts/Cross-entropy_method/IKw9N5IX">Cross-entropy method</a>: a general Monte Carlo approach to combinatorial and continuous multi-extremal optimization and <a href="/facts/Importance_sampling/jrbUnMXa">importance sampling</a></li> <li><a href="/facts/Differential_evolution/mcMagaB2">Differential evolution</a></li> <li><a href="/facts/Dynamic_Programming/CLcabtmk">Dynamic Programming</a>: problems exhibiting the properties of <a href="/facts/Overlapping_subproblem/6HhLdMe3">overlapping subproblems</a> and <a href="/facts/Optimal_substructure/GlfdqDfG">optimal substructure</a></li> <li><a href="/facts/Ellipsoid_method/K3SDpleG">Ellipsoid method</a>: is an algorithm for solving convex optimization problems</li> <li><a href="/facts/Evolutionary_computation/qXyxPI8j">Evolutionary computation</a>: optimization inspired by biological mechanisms of evolution <ul><li><a href="/facts/Evolution_strategy/88T0MMkv">Evolution strategy</a></li> <li><a href="/facts/Gene_expression_programming/jPvNjy6N">Gene expression programming</a></li> <li><a href="/facts/Genetic_algorithms/WP2AFWuW">Genetic algorithms</a> <ul><li><a href="/facts/Fitness_proportionate_selection/RSeQxJXS">Fitness proportionate selection</a> – also known as roulette-wheel selection</li> <li><a href="/facts/Stochastic_universal_sampling/NQM94tom">Stochastic universal sampling</a></li> <li><a href="/facts/Tournament_selection/Tmm4QRsV">Tournament selection</a></li> <li><a href="/facts/Truncation_selection/e9aFWxYf">Truncation selection</a></li></ul></li> <li><a href="/facts/Memetic_algorithm/m1oMttra">Memetic algorithm</a></li> <li><a href="/facts/Swarm_intelligence/fI8461G4">Swarm intelligence</a> <ul><li><a href="/facts/Ant_colony_optimization/SXGYs630">Ant colony optimization</a></li> <li><a href="/facts/Bees_algorithm/t8Vl9Peq">Bees algorithm</a>: a search algorithm which mimics the food foraging behavior of swarms of honey bees</li> <li><a href="/facts/Particle_swarm_optimization/QYo2YaP7">Particle swarm</a></li></ul></li></ul></li> <li><a href="/facts/Frank-Wolfe_algorithm/FqN0TxID">Frank-Wolfe algorithm</a>: an iterative first-order optimization algorithm for constrained convex optimization</li> <li><a href="/facts/Golden-section_search/vvXlfXeJ">Golden-section search</a>: an algorithm for finding the maximum of a real function</li> <li><a href="/facts/Gradient_descent/pFFrek0F">Gradient descent</a></li> <li><a href="/facts/Hyperparameter_optimization/bzcJJrxs">Grid Search</a></li> <li><a href="/facts/Harmony_search/6zoAh906">Harmony search</a> (HS): a <a href="/facts/Metaheuristic/ECF71Rez">metaheuristic</a> algorithm mimicking the improvisation process of musicians</li> <li>A hybrid HS-LS conjugate gradient algorithm (see <a href="https://doi.org/10.1016/j.cam.2023.115304">https://doi.org/10.1016/j.cam.2023.115304</a>)</li> <li><a href="/facts/Interior_point_method/prIIrceN">Interior point method</a></li> <li><a href="/facts/Line_search/GQWhNEsR">Line search</a></li> <li><a href="/facts/Linear_programming/GduXFQxT">Linear programming</a> <ul><li><a href="/facts/Benson%2527s_algorithm/dMGrFDSH">Benson's algorithm</a>: an algorithm for solving linear <a href="/facts/Vector_optimization/3Snb21Do">vector optimization</a> problems</li> <li><a href="/facts/Dantzig%25E2%2580%2593Wolfe_decomposition/Y9Y3F3Fz">Dantzig–Wolfe decomposition</a>: an algorithm for solving linear programming problems with special structure</li> <li><a href="/facts/Delayed_column_generation/3T355xua">Delayed column generation</a></li> <li><a href="/facts/Integer_linear_programming/MDaaadoA">Integer linear programming</a>: solve linear programming problems where some or all the unknowns are restricted to integer values <ul><li><a href="/facts/Branch_and_cut/YJ07W6eP">Branch and cut</a></li> <li><a href="/facts/Cutting-plane_method/8V7TTfhx">Cutting-plane method</a></li></ul></li> <li><a href="/facts/Karmarkar%2527s_algorithm/rprPV1Wu">Karmarkar's algorithm</a>: The first reasonably efficient algorithm that solves the <a href="/facts/Linear_programming/GduXFQxT">linear programming</a> problem in <a href="/facts/Polynomial_time/77T62gmf">polynomial time</a>.</li> <li><a href="/facts/Simplex_algorithm/9fndF6cq">Simplex algorithm</a>: an algorithm for solving <a href="/facts/Linear_programming/GduXFQxT">linear programming</a> problems</li></ul></li> <li><a href="/facts/Local_search_(optimization)/G1D2aHBz">Local search</a>: a metaheuristic for solving computationally hard optimization problems <ul><li><a href="/facts/Random-restart_hill_climbing/CMtyufA5">Random-restart hill climbing</a></li> <li><a href="/facts/Tabu_search/olw8qTSl">Tabu search</a></li></ul></li> <li><a href="/facts/Minimax/GcCTKutW">Minimax</a> used in game programming</li> <li><a href="/facts/Nearest_neighbor_search/R6QTyAph">Nearest neighbor search</a> (NNS): find closest points in a <a href="/facts/Metric_space/gnBBRXtc">metric space</a> <ul><li><a href="/facts/Best_Bin_First/pc0UzgSo">Best Bin First</a>: find an approximate solution to the <a href="/facts/Nearest_neighbor_search/R6QTyAph">nearest neighbor search</a> problem in very-high-dimensional spaces</li></ul></li> <li><a href="/facts/Newton%2527s_method_in_optimization/H46TN721">Newton's method in optimization</a></li> <li><a href="/facts/Nonlinear_optimization/cSXGuX2m">Nonlinear optimization</a> <ul><li><a href="/facts/BFGS_method/aA6KXo6h">BFGS method</a>: a <a href="/facts/Nonlinear_optimization/cSXGuX2m">nonlinear optimization</a> algorithm</li> <li><a href="/facts/Gauss%25E2%2580%2593Newton_algorithm/7c5en5cU">Gauss–Newton algorithm</a>: an algorithm for solving nonlinear <a href="/facts/Least_squares/50jIwbxC">least squares</a> problems</li> <li><a href="/facts/Levenberg%25E2%2580%2593Marquardt_algorithm/yqhqgb1g">Levenberg–Marquardt algorithm</a>: an algorithm for solving nonlinear <a href="/facts/Least_squares/50jIwbxC">least squares</a> problems</li> <li><a href="/facts/Nelder%25E2%2580%2593Mead_method/6aXswEax">Nelder–Mead method</a> (downhill simplex method): a <a href="/facts/Nonlinear_optimization/cSXGuX2m">nonlinear optimization</a> algorithm</li></ul></li> <li><a href="/facts/Odds_algorithm/7aAph2N6">Odds algorithm</a> (Bruss algorithm): Finds the optimal strategy to predict a last specific event in a random sequence event</li> <li><a href="/facts/Hyperparameter_optimization/bzcJJrxs">Random Search</a></li> <li><a href="/facts/Simulated_annealing/JCmHqd3t">Simulated annealing</a></li> <li><a href="/facts/Stochastic_tunneling/yAxlNskt">Stochastic tunneling</a></li> <li><a href="/facts/Subset_sum_problem/Guvrwy0L">Subset sum</a> algorithm</li></ul> <h2 id="computational-science">Computational science</h2> <p class="note">Further information: <a href="/facts/Computational_science/PnVD19hw">Computational science</a></p> <h3>Astronomy</h3> <ul><li><a href="/facts/Doomsday_algorithm/5TXr6fsc">Doomsday algorithm</a>: day of the week</li> <li>various <a href="/facts/Computus/HUosdPeP">Easter algorithms</a> are used to calculate the day of Easter</li> <li><a href="/facts/Zeller%2527s_congruence/qgktaxfI">Zeller's congruence</a> is an algorithm to calculate the day of the week for any Julian or Gregorian calendar date</li></ul> <h3>Bioinformatics</h3> <p class="note">Further information: <a href="/facts/Bioinformatics/D5x2L8ee">Bioinformatics</a></p> <p class="note">See also: Sequence alignment algorithms</p> <ul><li><a href="/facts/Basic_Local_Alignment_Search_Tool/uWufGxFH">Basic Local Alignment Search Tool</a> also known as BLAST: an algorithm for comparing primary biological sequence information</li> <li><a href="/facts/Bloom_filter/Gq2WVE37">Bloom Filter</a>: probabilistic data structure used to test for the existence of an element within a set. Primarily used in bioinformatics to test for the existence of a <a href="/facts/K-mer/0s3TbUHp">k-mer</a> in a sequence or sequences.</li> <li><a href="/facts/Kabsch_algorithm/UTs3sopK">Kabsch algorithm</a>: calculate the optimal alignment of two sets of points in order to compute the <a href="/facts/RMSD/MlQVhebp">root mean squared deviation</a> between two protein structures.</li> <li><a href="/facts/Maximum_parsimony_(phylogenetics)/sxccmrfR">Maximum parsimony (phylogenetics)</a>: an algorithm for finding the simplest phylogenetic tree to explain a given character matrix.</li> <li>Sorting by signed reversals: an algorithm for understanding genomic evolution.</li> <li><a href="/facts/UPGMA/XbJ1rIrl">UPGMA</a>: a distance-based phylogenetic tree construction algorithm.</li> <li><a href="/facts/Velvet_(algorithm)/nfBDEAl7">Velvet</a>: a set of algorithms manipulating <a href="/facts/De_Bruijn_graph/QKFsDeEw">de Bruijn graphs</a> for genomic <a href="/facts/Sequence_assembly/owEm30vn">sequence assembly</a></li></ul> <h3>Geoscience</h3> <p class="note">Further information: <a href="/facts/Geoscience/rQsXCSbM">Geoscience</a></p> <ul><li><a href="/facts/Geohash/zYeUQVes">Geohash</a>: a public domain algorithm that encodes a decimal latitude/longitude pair as a hash string</li> <li><a href="/facts/Vincenty%2527s_formulae/Rg491HTb">Vincenty's formulae</a>: a fast algorithm to calculate the distance between two latitude/longitude points on an ellipsoid</li></ul> <h3>Linguistics</h3> <p class="note">Further information: <a href="/facts/Computational_linguistics/XmegJ6LC">Computational linguistics</a> and <a href="/facts/Natural_language_processing/1hjMKsSN">Natural language processing</a></p> <ul><li><a href="/facts/Lesk_algorithm/UsVqWKNj">Lesk algorithm</a>: word sense disambiguation</li> <li><a href="/facts/Stemming/lqtKp4X7">Stemming algorithm</a>: a method of reducing words to their stem, base, or root form</li> <li><a href="/facts/Sukhotin%2527s_algorithm/EgaFdVBh">Sukhotin's algorithm</a>: a statistical classification algorithm for classifying characters in a text as vowels or consonants</li></ul> <h3>Medicine</h3> <p class="note">Further information: <a href="/facts/Medical_algorithms/KJRKL892">Medical algorithms</a></p> <ul><li><a href="/facts/ESC_algorithm/7fckX3Jm">ESC algorithm</a> for the diagnosis of heart failure</li> <li><a href="/facts/Manning_Criteria/H1ufYYUt">Manning Criteria</a> for irritable bowel syndrome</li> <li><a href="/facts/Pulmonary_embolism/LPjKCPba">Pulmonary embolism</a> diagnostic algorithms</li> <li><a href="/facts/Texas_Medication_Algorithm_Project/SpWEcjnd">Texas Medication Algorithm Project</a></li></ul> <h3>Physics</h3> <p class="note">Further information: <a href="/facts/Computational_physics/1ltJ109X">Computational physics</a></p> <ul><li><a href="/facts/Constraint_algorithm/nEFCcBlX">Constraint algorithm</a>: a class of algorithms for satisfying constraints for bodies that obey Newton's equations of motion</li> <li><a href="/facts/Demon_algorithm/xGtSVD5S">Demon algorithm</a>: a <a href="/facts/Monte_Carlo_method/AkHjY7jc">Monte Carlo method</a> for efficiently sampling members of a <a href="/facts/Microcanonical_ensemble/L4fE6SxT">microcanonical ensemble</a> with a given energy</li> <li><a href="/facts/Featherstone%2527s_algorithm/yERyP1kY">Featherstone's algorithm</a>: computes the effects of forces applied to a structure of joints and links</li> <li><a href="/facts/Glauber_dynamics/fRg4wJ9p">Glauber dynamics</a>: a method for simulating the Ising Model on a computer</li> <li><a href="/facts/Ground_state/ML7cfCug">Ground state</a> approximation <ul><li><a href="/facts/Variational_method/Ya5Lsma3">Variational method</a> <ul><li><a href="/facts/Ritz_method/tIn6wYKM">Ritz method</a></li></ul></li></ul></li> <li><a href="/facts/N-body_problem/5goGsW5x"><i>n</i>-body problems</a> <ul><li><a href="/facts/Barnes%25E2%2580%2593Hut_simulation/bsxHpaYb">Barnes–Hut simulation</a>: Solves the n-body problem in an approximate way that has the order O(n log n) instead of O(n2) as in a direct-sum simulation.</li> <li><a href="/facts/Fast_multipole_method/fpUr8vsp">Fast multipole method</a> (FMM): speeds up the calculation of long-ranged forces</li></ul></li> <li><a href="/facts/Rainflow-counting_algorithm/QtNkMx0Y">Rainflow-counting algorithm</a>: Reduces a complex <a href="/facts/Stress_(physics)/ErAXDbbd">stress</a> history to a count of elementary stress-reversals for use in <a href="/facts/Fatigue_(material)/zmJY8hMt">fatigue</a> analysis</li> <li><a href="/facts/Sweep_and_prune/lXG96NCU">Sweep and prune</a>: a broad phase algorithm used during <a href="/facts/Collision_detection/kXkE9WXv">collision detection</a> to limit the number of pairs of solids that need to be checked for collision</li> <li><a href="/facts/VEGAS_algorithm/2uyormme">VEGAS algorithm</a>: a method for reducing error in <a href="/facts/Monte_Carlo_simulation/AkHjY7jc">Monte Carlo simulations</a></li></ul> <h3>Statistics</h3> <p class="note">Further information: <a href="/facts/Computational_statistics/JnD0zQDl">Computational statistics</a></p> <ul><li><a href="/facts/Algorithms_for_calculating_variance/pSYpl5VM">Algorithms for calculating variance</a>: avoiding instability and numerical overflow</li> <li><a href="/facts/Approximate_counting_algorithm/qj40YmgP">Approximate counting algorithm</a>: allows counting large number of events in a small register</li> <li><a href="/facts/Bayesian_statistics/9w7b1Bw4">Bayesian statistics</a> <ul><li><a href="/facts/Nested_sampling_algorithm/tpmHrePe">Nested sampling algorithm</a>: a computational approach to the problem of comparing models in Bayesian statistics</li></ul></li> <li><a href="/facts/Data_clustering/HUeDnWPt">Clustering algorithms</a> <ul><li><a href="/facts/UPGMA/XbJ1rIrl">Average-linkage clustering</a>: a simple agglomerative clustering algorithm</li> <li><a href="/facts/Canopy_clustering_algorithm/aTaptUFD">Canopy clustering algorithm</a>: an unsupervised pre-clustering algorithm related to the K-means algorithm</li> <li><a href="/facts/Chinese_whispers_(clustering_method)/gsFNXwJq">Chinese whispers</a></li> <li><a href="/facts/Complete-linkage_clustering/Ir4PLgKm">Complete-linkage clustering</a>: a simple agglomerative clustering algorithm</li> <li><a href="/facts/DBSCAN/EKKoHRkM">DBSCAN</a>: a density based clustering algorithm</li> <li><a href="/facts/Expectation-maximization_algorithm/32P2bdBc">Expectation-maximization algorithm</a></li> <li><a href="/facts/Fuzzy_clustering/MEmTL2po">Fuzzy clustering</a>: a class of clustering algorithms where each point has a degree of belonging to clusters <ul><li><a href="/facts/FLAME_clustering/TKHNG1KQ">FLAME clustering</a> (Fuzzy clustering by Local Approximation of MEmberships): define clusters in the dense parts of a dataset and perform cluster assignment solely based on the neighborhood relationships among objects</li> <li><a href="/facts/Fuzzy_clustering/MEmTL2po">Fuzzy c-means</a></li></ul></li> <li><a href="/facts/K-means_clustering/vxIcqHwN">k-means clustering</a>: cluster objects based on attributes into partitions</li> <li><a href="/facts/K-means%252B%252B/llIf37JH">k-means++</a>: a variation of this, using modified random seeds</li> <li><a href="/facts/K-medoids/YFYaESyy">k-medoids</a>: similar to k-means, but chooses datapoints or <a href="/facts/Medoid/E4k3V72p">medoids</a> as centers</li> <li><a href="/facts/KHOPCA_clustering_algorithm/9tL8aS7a">KHOPCA clustering algorithm</a>: a local clustering algorithm, which produces hierarchical multi-hop clusters in static and mobile environments.</li> <li><a href="/facts/Linde%25E2%2580%2593Buzo%25E2%2580%2593Gray_algorithm/CINLdkcl">Linde–Buzo–Gray algorithm</a>: a vector quantization algorithm to derive a good codebook</li> <li><a href="/facts/Lloyd%2527s_algorithm/LuersNRa">Lloyd's algorithm</a> (Voronoi iteration or relaxation): group data points into a given number of categories, a popular algorithm for <a href="/facts/K-means_clustering/vxIcqHwN">k-means clustering</a></li> <li><a href="/facts/OPTICS_algorithm/NqbewAnI">OPTICS</a>: a density based clustering algorithm with a visual evaluation method</li> <li><a href="/facts/Single-linkage_clustering/suwgF2yb">Single-linkage clustering</a>: a simple agglomerative clustering algorithm</li> <li><a href="/facts/SUBCLU/lT4LRwwL">SUBCLU</a>: a subspace clustering algorithm</li> <li><a href="/facts/WACA_clustering_algorithm/4yMAFMuF">WACA clustering algorithm</a>: a local clustering algorithm with potentially multi-hop structures; for dynamic networks</li> <li><a href="/facts/Ward%2527s_method/LIRt8Ir4">Ward's method</a>: an agglomerative clustering algorithm, extended to more general Lance–Williams algorithms</li></ul></li> <li><a href="/facts/Estimation_theory/4nbgFDec">Estimation Theory</a> <ul><li><a href="/facts/Expectation-maximization_algorithm/32P2bdBc">Expectation-maximization algorithm</a> A class of related algorithms for finding maximum likelihood estimates of parameters in probabilistic models <ul><li><a href="/facts/Ordered_subset_expectation_maximization/roNxKkQj">Ordered subset expectation maximization</a> (OSEM): used in <a href="/facts/Medical_imaging/pL6JyJEp">medical imaging</a> for <a href="/facts/Positron_emission_tomography/5SmcW6qz">positron emission tomography</a>, <a href="/facts/Single-photon_emission_computed_tomography/ag6of05C">single-photon emission computed tomography</a> and <a href="/facts/X-ray/wseP79cN">X-ray</a> computed tomography.</li></ul></li> <li><a href="/facts/Kalman_filter/wNK7rnbk">Kalman filter</a>: estimate the state of a linear <a href="/facts/Dynamical_system/782gREl5">dynamic system</a> from a series of noisy measurements</li> <li><a href="/facts/Odds_algorithm/7aAph2N6">Odds algorithm</a> (Bruss algorithm) Optimal online search for distinguished value in sequential random input</li></ul></li> <li><a href="/facts/False_nearest_neighbor_algorithm/Wa5y2UuX">False nearest neighbor algorithm</a> (FNN) estimates <a href="/facts/Fractal_dimension/pJ9tVnwn">fractal dimension</a></li> <li><a href="/facts/Hidden_Markov_model/ur1zTAhP">Hidden Markov model</a> <ul><li><a href="/facts/Baum%25E2%2580%2593Welch_algorithm/8kW1Ajxx">Baum–Welch algorithm</a>: computes maximum likelihood estimates and <a href="/facts/Maximum_a_posteriori/Y5zHyqfX">posterior mode</a> estimates for the parameters of a hidden Markov model</li> <li><a href="/facts/Forward-backward_algorithm/3tVWYLSH">Forward-backward algorithm</a>: a dynamic programming algorithm for computing the probability of a particular observation sequence</li> <li><a href="/facts/Viterbi_algorithm/FYoyJ6YY">Viterbi algorithm</a>: find the most likely sequence of hidden states in a hidden Markov model</li></ul></li> <li><a href="/facts/Partial_least_squares_regression/jYIcInPw">Partial least squares regression</a>: finds a linear model describing some predicted variables in terms of other observable variables</li> <li><a href="/facts/Queuing_theory/8NDl56EM">Queuing theory</a> <ul><li><a href="/facts/Buzen%2527s_algorithm/vwakTqpn">Buzen's algorithm</a>: an algorithm for calculating the normalization constant G(K) in the <a href="/facts/Gordon%25E2%2580%2593Newell_theorem/rkbWqHcY">Gordon–Newell theorem</a></li></ul></li> <li><a href="/facts/RANSAC/soUk14qR">RANSAC</a> (an abbreviation for "RANdom SAmple Consensus"): an iterative method to estimate parameters of a mathematical model from a set of observed data which contains outliers</li> <li><a href="/facts/Scoring_algorithm/H6PFm0mp">Scoring algorithm</a>: is a form of <a href="/facts/Newton%2527s_method/VlRhI2FL">Newton's method</a> used to solve <a href="/facts/Maximum_likelihood/0Yq2dpQD">maximum likelihood</a> equations numerically</li> <li><a href="/facts/Yamartino_method/Xw0UCb7W">Yamartino method</a>: calculate an approximation to the standard deviation σθ of wind direction θ during a single pass through the incoming data</li> <li><a href="/facts/Ziggurat_algorithm/g0ltMb3h">Ziggurat algorithm</a>: generates random numbers from a non-uniform distribution</li></ul> <h2 id="computer-science">Computer science</h2> <p class="note">Further information: <a href="/facts/Computer_science/lN3pEyPz">Computer science</a></p> <h3>Computer architecture</h3> <p class="note">Further information: <a href="/facts/Computer_architecture/tHtwxgR2">Computer architecture</a></p> <ul><li><a href="/facts/Tomasulo_algorithm/Ro81atJm">Tomasulo algorithm</a>: allows sequential instructions that would normally be stalled due to certain dependencies to execute non-sequentially</li></ul> <h3>Computer graphics</h3> <p class="note">Further information: <a href="/facts/Computer_graphics/lapBE8wv">Computer graphics</a></p> <ul><li><a href="/facts/Binary_space_partitioning/sn9MhTSB">Binary space partitioning</a></li> <li><a href="/facts/Clipping_(computer_graphics)/xpPsC6Ax">Clipping</a> <ul><li><a href="/facts/Line_clipping/t3Hsx3lf">Line clipping</a> <ul><li><a href="/facts/Cohen%25E2%2580%2593Sutherland/ovd134lS">Cohen–Sutherland</a></li> <li><a href="/facts/Cyrus%25E2%2580%2593Beck/oNsWcYfu">Cyrus–Beck</a></li> <li><a href="/facts/Fast_clipping/t3Hsx3lf">Fast-clipping</a></li> <li><a href="/facts/Liang%25E2%2580%2593Barsky_algorithm/0YHgWffe">Liang–Barsky</a></li> <li><a href="/facts/Nicholl%25E2%2580%2593Lee%25E2%2580%2593Nicholl/SCgRkGSL">Nicholl–Lee–Nicholl</a></li></ul></li> <li>Polygon clipping <ul><li><a href="/facts/Sutherland%25E2%2580%2593Hodgman/WDrYbGUl">Sutherland–Hodgman</a></li> <li><a href="/facts/Vatti_clipping_algorithm/TVqPvjA2">Vatti</a></li> <li><a href="/facts/Weiler%25E2%2580%2593Atherton/zHnWENLa">Weiler–Atherton</a></li></ul></li></ul></li> <li><a href="/facts/Contour_line/35Qten5r">Contour lines</a> and <a href="/facts/Isosurface/kvMHSemB">Isosurfaces</a> <ul><li><a href="/facts/Marching_cubes/mYbQyPYD">Marching cubes</a>: extract a polygonal mesh of an isosurface from a three-dimensional scalar field (sometimes called voxels)</li> <li><a href="/facts/Marching_squares/JdlWLo2l">Marching squares</a>: generates contour lines for a two-dimensional scalar field</li> <li><a href="/facts/Marching_tetrahedrons/YqPEr64H">Marching tetrahedrons</a>: an alternative to <a href="/facts/Marching_cubes/mYbQyPYD">Marching cubes</a></li></ul></li> <li>Discrete Green's theorem: is an algorithm for computing double integral over a generalized rectangular domain in constant time. It is a natural extension to the summed area table algorithm</li> <li><a href="/facts/Flood_fill/ehcLrEBg">Flood fill</a>: fills a connected region of a multi-dimensional array with a specified symbol</li> <li><a href="/facts/Global_illumination/CbQX6CWM">Global illumination</a> algorithms: Considers direct illumination and reflection from other objects. <ul><li><a href="/facts/Ambient_occlusion/oeEEyb2x">Ambient occlusion</a></li> <li><a href="/facts/Beam_tracing/Cc4zjIQ5">Beam tracing</a></li> <li><a href="/facts/Cone_tracing/Na7nS04J">Cone tracing</a></li> <li><a href="/facts/Image-based_lighting/dlQ28BYA">Image-based lighting</a></li> <li><a href="/facts/Metropolis_light_transport/wRoPqI2f">Metropolis light transport</a></li> <li><a href="/facts/Path_tracing/fxhaM84b">Path tracing</a></li> <li><a href="/facts/Photon_mapping/t58p6V7w">Photon mapping</a></li> <li><a href="/facts/Radiosity_(3D_computer_graphics)/qN75qQgV">Radiosity</a></li> <li><a href="/facts/Ray_tracing_(graphics)/n6qpap2q">Ray tracing</a></li></ul></li> <li><a href="/facts/Hidden-surface_determination/hk9dqmDE">Hidden-surface removal</a> or visual surface determination <ul><li><a href="/facts/Newell%2527s_algorithm/pxUpwmDk">Newell's algorithm</a>: eliminate polygon cycles in the depth sorting required in hidden-surface removal</li> <li><a href="/facts/Painter%2527s_algorithm/rA9wMkaA">Painter's algorithm</a>: detects visible parts of a 3-dimensional scenery</li> <li><a href="/facts/Scanline_rendering/nmJC2rbn">Scanline rendering</a>: constructs an image by moving an imaginary line over the image</li> <li><a href="/facts/Warnock_algorithm/3I1tq1SF">Warnock algorithm</a></li></ul></li> <li><a href="/facts/Line_drawing_algorithm/elNM0J2u">Line drawing</a>: graphical algorithm for approximating a line segment on discrete graphical media. <ul><li><a href="/facts/Bresenham%2527s_line_algorithm/G1fcMKEF">Bresenham's line algorithm</a>: plots points of a 2-dimensional array to form a straight line between 2 specified points (uses decision variables)</li> <li><a href="/facts/Digital_differential_analyzer_(graphics_algorithm)/hBPl8mQR">DDA line algorithm</a>: plots points of a 2-dimensional array to form a straight line between specified points</li> <li><a href="/facts/Xiaolin_Wu%2527s_line_algorithm/ntk2b6zN">Xiaolin Wu's line algorithm</a>: algorithm for line antialiasing.</li></ul></li> <li><a href="/facts/Midpoint_circle_algorithm/6CSNdb6t">Midpoint circle algorithm</a>: an algorithm used to determine the points needed for drawing a circle</li> <li><a href="/facts/Ramer%25E2%2580%2593Douglas%25E2%2580%2593Peucker_algorithm/VT31304N">Ramer–Douglas–Peucker algorithm</a>: Given a 'curve' composed of line segments to find a curve not too dissimilar but that has fewer points</li> <li><a href="/facts/Shading/ewcDEfda">Shading</a> <ul><li><a href="/facts/Gouraud_shading/04Nz96F5">Gouraud shading</a>: an algorithm to simulate the differing effects of light and colour across the surface of an object in 3D computer graphics</li> <li><a href="/facts/Phong_shading/gTMGmw27">Phong shading</a>: an algorithm to interpolate surface normal-vectors for surface shading in 3D computer graphics</li></ul></li> <li><a href="/facts/Slerp/A40A6390">Slerp</a> (spherical linear interpolation): quaternion interpolation for the purpose of animating 3D rotation</li> <li><a href="/facts/Summed_area_table/HUba1xXR">Summed area table</a> (also known as an integral image): an algorithm for computing the sum of values in a rectangular subset of a grid in constant time</li></ul> <h3>Cryptography</h3> <p class="note">Further information: <a href="/facts/Cryptography/e94PEVau">Cryptography</a> and <a href="/facts/Topics_in_cryptography/E6r9ID3G">Topics in cryptography</a></p> <ul><li><a href="/facts/Asymmetric_key_algorithm/gowoFTxS">Asymmetric (public key) encryption</a>: <ul><li><a href="/facts/ElGamal_encryption/sKDVyMyR">ElGamal</a></li> <li><a href="/facts/Elliptic_curve_cryptography/YbjcXIWk">Elliptic curve cryptography</a></li> <li>MAE1</li> <li><a href="/facts/NTRUEncrypt/B6MR5HkI">NTRUEncrypt</a></li> <li><a href="/facts/RSA_(cryptosystem)/XTzyfHuq">RSA</a></li></ul></li> <li><a href="/facts/Digital_signature/tY7e2pnW">Digital signatures</a> (asymmetric authentication): <ul><li><a href="/facts/Digital_Signature_Algorithm/0o0FK486">DSA</a>, and its variants: <ul><li><a href="/facts/ECDSA/gl0mfnS1">ECDSA</a> and Deterministic ECDSA</li> <li><a href="/facts/EdDSA/IbTRBhK3">EdDSA</a> (Ed25519)</li></ul></li> <li><a href="/facts/RSA_(cryptosystem)/XTzyfHuq">RSA</a></li></ul></li> <li><a href="/facts/Cryptographic_hash_function/cuxkgbST">Cryptographic hash functions</a> (see also the section on message authentication codes): <ul><li><a href="/facts/BLAKE_(hash_function)/3QuBJ24f">BLAKE</a></li> <li><a href="/facts/MD5/8WIXb9Dq">MD5</a> – Note that there is now a method of generating collisions for MD5</li> <li><a href="/facts/RIPEMD-160/z09kTSWX">RIPEMD-160</a></li> <li><a href="/facts/SHA-1/LDYCV1je">SHA-1</a> – Note that there is now a method of generating collisions for SHA-1</li> <li><a href="/facts/SHA-2/P59oPeGq">SHA-2</a> (SHA-224, SHA-256, SHA-384, SHA-512)</li> <li><a href="/facts/SHA-3/bA3BCp7K">SHA-3</a> (SHA3-224, SHA3-256, SHA3-384, SHA3-512, SHAKE128, SHAKE256)</li> <li><a href="/facts/Tiger_(hash_function)/xLMxNVV5">Tiger</a> (TTH), usually used in <a href="/facts/Hash_tree_(persistent_data_structure)/YqxhuTTM">Tiger tree hashes</a></li> <li><a href="/facts/WHIRLPOOL/5d6erXP3">WHIRLPOOL</a></li></ul></li> <li><a href="/facts/Cryptographically_secure_pseudo-random_number_generator/Kew9SdpN">Cryptographically secure pseudo-random number generators</a> <ul><li><a href="/facts/Blum_Blum_Shub/aWEKXsnX">Blum Blum Shub</a> – based on the hardness of <a href="/facts/Integer_factorization/EjMCTz2t">factorization</a></li> <li><a href="/facts/Fortuna_(PRNG)/g8XGvI0s">Fortuna</a>, intended as an improvement on <a href="/facts/Yarrow_algorithm/HvkbQysb">Yarrow algorithm</a></li> <li><a href="/facts/Linear-feedback_shift_register/22pktBbX">Linear-feedback shift register</a> (note: many LFSR-based algorithms are weak or have been broken)</li> <li><a href="/facts/Yarrow_algorithm/HvkbQysb">Yarrow algorithm</a></li></ul></li> <li><a href="/facts/Key_exchange/gcYhnpFb">Key exchange</a> <ul><li><a href="/facts/Diffie%25E2%2580%2593Hellman_key_exchange/xR4YQcaD">Diffie–Hellman key exchange</a></li> <li><a href="/facts/Elliptic-curve_Diffie%25E2%2580%2593Hellman/zy3IJCeK">Elliptic-curve Diffie–Hellman</a> (ECDH)</li></ul></li> <li><a href="/facts/Key_derivation_function/3jL2jTTb">Key derivation functions</a>, often used for <a href="/facts/Password_hashing/3jL2jTTb">password hashing</a> and <a href="/facts/Key_stretching/uVQSNI4H">key stretching</a> <ul><li><a href="/facts/Argon2/8sAkGSch">Argon2</a></li> <li><a href="/facts/Bcrypt/2hWjME4U">bcrypt</a></li> <li><a href="/facts/PBKDF2/nIq55BCh">PBKDF2</a></li> <li><a href="/facts/Scrypt/StlAggdS">scrypt</a></li></ul></li> <li><a href="/facts/Message_authentication_code/mXxCP5Yl">Message authentication codes</a> (symmetric authentication algorithms, which take a key as a parameter): <ul><li><a href="/facts/Keyed-hash_message_authentication_code/Qy9WD4V9">HMAC</a>: keyed-hash message authentication</li> <li><a href="/facts/Poly1305/xlqUKmWX">Poly1305</a></li> <li><a href="/facts/SipHash/snDLDp73">SipHash</a></li></ul></li> <li><a href="/facts/Secret_sharing/umC4t0cD">Secret sharing</a>, secret splitting, key splitting, M of N algorithms <ul><li>Blakey's scheme</li> <li><a href="/facts/Shamir%2527s_secret_sharing/dv5yFFHY">Shamir's secret sharing</a></li></ul></li> <li><a href="/facts/Symmetric_key_algorithm/5zfe0b76">Symmetric (secret key) encryption</a>: <ul><li><a href="/facts/Advanced_Encryption_Standard/HdXGBY2Q">Advanced Encryption Standard</a> (AES), winner of <a href="/facts/NIST/gr9Fnh85">NIST</a> competition, also known as <a href="/facts/Rijndael/HdXGBY2Q">Rijndael</a></li> <li><a href="/facts/Blowfish_(cipher)/H6fYatpd">Blowfish</a></li> <li><a href="/facts/Salsa20/gQjhIf2M">ChaCha20</a> updated variant of Salsa20</li> <li><a href="/facts/Data_Encryption_Standard/STfBjTGb">Data Encryption Standard</a> (DES), sometimes DE Algorithm, winner of NBS selection competition, replaced by AES for most purposes</li> <li><a href="/facts/International_Data_Encryption_Algorithm/HuRBKLQY">IDEA</a></li> <li><a href="/facts/RC4_(cipher)/HAR5kL0T">RC4 (cipher)</a></li> <li><a href="/facts/Salsa20/gQjhIf2M">Salsa20</a></li> <li><a href="/facts/Threefish/xGnFbEtW">Threefish</a></li> <li><a href="/facts/Tiny_Encryption_Algorithm/aaFnFgKo">Tiny Encryption Algorithm</a> (TEA)</li> <li><a href="/facts/Twofish/T1pjlttA">Twofish</a></li></ul></li> <li><a href="/facts/Post-quantum_cryptography/1qeqUQve">Post-quantum cryptography</a></li> <li><a href="/facts/Proof-of-work_system/GKI1LcQU">Proof-of-work algorithms</a></li></ul> <h3>Digital logic</h3> <ul><li>Boolean minimization <ul><li><a href="/facts/Espresso_heuristic_logic_minimizer/nXDA6pv0">Espresso heuristic logic minimizer</a>: a fast algorithm for Boolean function minimization</li> <li><a href="/facts/Petrick%2527s_method/K0efVoER">Petrick's method</a>: another algorithm for Boolean simplification</li> <li><a href="/facts/Quine%25E2%2580%2593McCluskey_algorithm/pXl5Ezor">Quine–McCluskey algorithm</a>: also called as Q-M algorithm, programmable method for simplifying the Boolean equations</li></ul></li></ul> <h3>Machine learning and statistical classification</h3> <p class="note">Main article: <a href="/facts/List_of_machine_learning_algorithms/0Vxx79yj">List of machine learning algorithms</a></p> <p class="note">Further information: <a href="/facts/Machine_learning/e0w0XJTu">Machine learning</a> and <a href="/facts/Statistical_classification/jXXHRkXR">Statistical classification</a></p> <ul><li><a href="/facts/Almeida%25E2%2580%2593Pineda_recurrent_backpropagation/8chtukzf">Almeida–Pineda recurrent backpropagation</a>: Adjust a matrix of synaptic weights to generate desired outputs given its inputs</li> <li><a href="/facts/ALOPEX/LW3Qcl2X">ALOPEX</a>: a correlation-based <a href="/facts/Machine_learning/e0w0XJTu">machine-learning algorithm</a></li> <li><a href="/facts/Association_rule_learning/oX6w9Kux">Association rule learning</a>: discover interesting relations between variables, used in <a href="/facts/Data_mining/AH53q5ac">data mining</a> <ul><li><a href="/facts/Apriori_algorithm/CNzfApBD">Apriori algorithm</a></li> <li><a href="/facts/Eclat_algorithm/oX6w9Kux">Eclat algorithm</a></li> <li><a href="/facts/Association_rule_learning/oX6w9Kux">FP-growth algorithm</a></li> <li><a href="/facts/One-attribute_rule/oX6w9Kux">One-attribute rule</a></li> <li><a href="/facts/Association_rule_learning/oX6w9Kux">Zero-attribute rule</a></li></ul></li> <li><a href="/facts/Boosting_(meta-algorithm)/HgejTPPu">Boosting (meta-algorithm)</a>: Use many weak learners to boost effectiveness <ul><li><a href="/facts/AdaBoost/nwJ6znVj">AdaBoost</a>: adaptive boosting</li> <li><a href="/facts/BrownBoost/gQF7ppcz">BrownBoost</a>: a boosting algorithm that may be robust to noisy datasets</li> <li><a href="/facts/LogitBoost/NkSv9MT9">LogitBoost</a>: <a href="/facts/Logistic_regression/mGj6mc8y">logistic regression</a> boosting</li> <li><a href="/facts/LPBoost/9pw3BqMj">LPBoost</a>: <a href="/facts/Linear_programming/GduXFQxT">linear programming</a> boosting</li></ul></li> <li><a href="/facts/Bootstrap_aggregating/EcIjuS4x">Bootstrap aggregating</a> (bagging): technique to improve stability and classification accuracy</li> <li><a href="/facts/Cluster_analysis/HUeDnWPt">Clustering</a>: a class of <a href="/facts/Unsupervised_learning/8a6f61MC">unsupervised learning</a> algorithms for grouping and bucketing related input vector</li> <li><a href="/facts/Computer_Vision/Tl2Yyk66">Computer Vision</a> <ul><li><a href="/facts/Grabcut/29eYqTBP">Grabcut</a> based on <a href="/facts/Graph_cuts_in_computer_vision/czXstoTB">Graph cuts</a></li></ul></li> <li><a href="/facts/Decision_tree_learning/LbPMAwdI">Decision Trees</a> <ul><li><a href="/facts/C4.5_algorithm/GGsxBTtz">C4.5 algorithm</a>: an extension to ID3</li> <li><a href="/facts/ID3_algorithm/cey9VCT7">ID3 algorithm</a> (Iterative Dichotomiser 3): use heuristic to generate small decision trees</li></ul></li> <li><a href="/facts/K-nearest_neighbors/Bs1UaAmE">k-nearest neighbors</a> (k-NN): a non-parametric method for classifying objects based on closest training examples in the <a href="/facts/Feature_space/nzAhYxfu">feature space</a></li> <li><a href="/facts/Linde%25E2%2580%2593Buzo%25E2%2580%2593Gray_algorithm/CINLdkcl">Linde–Buzo–Gray algorithm</a>: a vector quantization algorithm used to derive a good codebook</li> <li><a href="/facts/Locality-sensitive_hashing/hj8UllQG">Locality-sensitive hashing</a> (LSH): a method of performing probabilistic dimension reduction of high-dimensional data</li> <li><a href="/facts/Artificial_neural_network/6V1jMlkx">Neural Network</a> <ul><li><a href="/facts/Backpropagation/lCsIdKHc">Backpropagation</a>: a <a href="/facts/Supervised_learning/JlNFNPFt">supervised learning</a> method which requires a teacher that knows, or can calculate, the desired output for any given input</li> <li><a href="/facts/Hopfield_net/xUBr6rpm">Hopfield net</a>: a <a href="/facts/Recurrent_neural_network/bx7hBVB1">Recurrent neural network</a> in which all connections are symmetric</li> <li><a href="/facts/Perceptron/ArxdkAC1">Perceptron</a>: the simplest kind of feedforward neural network: a <a href="/facts/Linear_classifier/vsE823wQ">linear classifier</a>.</li> <li><a href="/facts/Pulse-coupled_neural_networks/HHkVxtUj">Pulse-coupled neural networks</a> (PCNN): <a href="/facts/Artificial_neural_network/6V1jMlkx">Neural models</a> proposed by modeling a cat's <a href="/facts/Visual_cortex/qmF8F5Sb">visual cortex</a> and developed for high-performance <a href="/facts/Bionics/ht3GueDP">biomimetic</a> image processing.</li> <li><a href="/facts/Radial_basis_function_network/KBesEWD3">Radial basis function network</a>: an artificial neural network that uses radial <a href="/facts/Basis_function/Bt7jqjY2">basis functions</a> as activation functions</li> <li><a href="/facts/Self-organizing_map/uuMRbpkl">Self-organizing map</a>: an unsupervised network that produces a low-dimensional representation of the input space of the training samples</li></ul></li> <li><a href="/facts/Random_forest/Ff1ppJEQ">Random forest</a>: classify using many decision trees</li> <li><a href="/facts/Reinforcement_learning/NrgPPS0Q">Reinforcement learning</a>: <ul><li><a href="/facts/Q-learning/emySKrgI">Q-learning</a>: learns an action-value function that gives the expected utility of taking a given action in a given state and following a fixed policy thereafter</li> <li><a href="/facts/State%25E2%2580%2593action%25E2%2580%2593reward%25E2%2580%2593state%25E2%2580%2593action/kmv4vSKG">State–Action–Reward–State–Action</a> (SARSA): learn a <a href="/facts/Markov_decision_process/cVlWIDrw">Markov decision process</a> policy</li> <li><a href="/facts/Temporal_difference_learning/FJDMDwBD">Temporal difference learning</a></li></ul></li> <li><a href="/facts/Relevance_vector_machine/rIz41WeL">Relevance-Vector Machine</a> (RVM): similar to SVM, but provides probabilistic classification</li> <li><a href="/facts/Supervised_learning/JlNFNPFt">Supervised learning</a>: Learning by examples (labelled data-set split into training-set and test-set)</li> <li><a href="/facts/Support_vector_machine/XobxpdBG">Support Vector Machine</a> (SVM): a set of methods which divide multidimensional data by finding a dividing hyperplane with the maximum margin between the two sets <ul><li><a href="/facts/Structured_SVM/kKIH061u">Structured SVM</a>: allows training of a classifier for general structured output labels.</li></ul></li> <li><a href="/facts/Winnow_algorithm/Shdmb7AD">Winnow algorithm</a>: related to the perceptron, but uses a <a href="/facts/Multiplicative_Weight_Update_Method/1gpChueb">multiplicative weight-update scheme</a></li></ul> <h3>Programming language theory</h3> <p class="note">Further information: <a href="/facts/Programming_language_theory/MfecfTFI">Programming language theory</a></p> <ul><li>C3 linearization: an algorithm used primarily to obtain a consistent linearization of a multiple inheritance hierarchy in object-oriented programming</li> <li><a href="/facts/Chaitin%2527s_algorithm/B4DSxHxV">Chaitin's algorithm</a>: a bottom-up, graph coloring register allocation algorithm that uses cost/degree as its spill metric</li> <li><a href="/facts/Hindley-Milner_type_inference/9GIuBwQ6">Hindley–Milner type inference algorithm</a></li> <li><a href="/facts/Rete_algorithm/Uw85WXLm">Rete algorithm</a>: an efficient pattern matching algorithm for implementing <a href="/facts/Start_symbol_(formal_languages)/QLxaQNAz">production rule</a> systems</li> <li><a href="/facts/Sethi-Ullman_algorithm/L56k6Mh4">Sethi-Ullman algorithm</a>: generates optimal code for arithmetic expressions</li></ul> <h4>Parsing</h4> <p class="note">Further information: <a href="/facts/Parsing/nRKB01S3">Parsing</a></p> <ul><li><a href="/facts/CYK_algorithm/W2J1SJ9z">CYK algorithm</a>: an O(n3) algorithm for parsing <a href="/facts/Context-free_grammar/yu1FFdK4">context-free grammars</a> in <a href="/facts/Chomsky_normal_form/eSDmphV6">Chomsky normal form</a></li> <li><a href="/facts/Earley_parser/b8XkRfW2">Earley parser</a>: another O(n3) algorithm for parsing any <a href="/facts/Context-free_grammar/yu1FFdK4">context-free grammar</a></li> <li><a href="/facts/GLR_parser/Pn3I1AYt">GLR parser</a>: an algorithm for parsing any <a href="/facts/Context-free_grammar/yu1FFdK4">context-free grammar</a> by <a href="/facts/Masaru_Tomita/q80rd8bB">Masaru Tomita</a>. It is tuned for deterministic grammars, on which it performs almost <a href="/facts/Linear_time/77T62gmf">linear time</a> and O(n3) in worst case.</li> <li><a href="/facts/Inside-outside_algorithm/6QNqgS2w">Inside-outside algorithm</a>: an O(n3) algorithm for re-estimating production probabilities in <a href="/facts/Probabilistic_context-free_grammar/84Ps7P9j">probabilistic context-free grammars</a></li> <li><a href="/facts/Lexical_analysis/T1JYWpIf">Lexical analysis</a></li> <li><a href="/facts/LL_parser/ot65DwYm">LL parser</a>: a relatively simple <a href="/facts/Linear_time/77T62gmf">linear time</a> parsing algorithm for a limited class of <a href="/facts/Context-free_grammar/yu1FFdK4">context-free grammars</a></li> <li><a href="/facts/LR_parser/bpMod8K0">LR parser</a>: A more complex <a href="/facts/Linear_time/77T62gmf">linear time</a> parsing algorithm for a larger class of <a href="/facts/Context-free_grammar/yu1FFdK4">context-free grammars</a>. Variants: <ul><li><a href="/facts/Canonical_LR_parser/Wr9MvcIn">Canonical LR parser</a></li> <li><a href="/facts/Look-ahead_LR_parser/4ey0KkTU">LALR (look-ahead LR) parser</a></li> <li><a href="/facts/Operator-precedence_parser/YHfocsFq">Operator-precedence parser</a></li> <li><a href="/facts/Simple_LR_parser/VaBjqE0y">Simple LR parser</a></li> <li><a href="/facts/Simple_precedence_parser/IoUtzCE2">Simple precedence parser</a></li></ul></li> <li><a href="/facts/Packrat_parser/8XdfJ7D0">Packrat parser</a>: a <a href="/facts/Linear_time/77T62gmf">linear time</a> parsing algorithm supporting some <a href="/facts/Context-free_grammar/yu1FFdK4">context-free grammars</a> and <a href="/facts/Parsing_expression_grammar/8XdfJ7D0">parsing expression grammars</a></li> <li><a href="/facts/Pratt_parser/YHfocsFq">Pratt parser</a></li> <li><a href="/facts/Recursive_descent_parser/ARhcuAv1">Recursive descent parser</a>: a <a href="/facts/Top-down_parsing/VVqphs5y">top-down parser</a> suitable for LL(<i>k</i>) grammars</li> <li><a href="/facts/Shunting-yard_algorithm/zIsL1fLk">Shunting-yard algorithm</a>: converts an infix-notation math expression to postfix</li></ul> <h3>Quantum algorithms</h3> <p class="note">Further information: <a href="/facts/Quantum_algorithm/ceJaJ6Eq">Quantum algorithm</a></p> <ul><li><a href="/facts/Deutsch%25E2%2580%2593Jozsa_algorithm/DKP9zCSC">Deutsch–Jozsa algorithm</a>: criterion of balance for Boolean function</li> <li><a href="/facts/Grover%2527s_algorithm/SJuxBPpA">Grover's algorithm</a>: provides quadratic speedup for many search problems</li> <li><a href="/facts/Shor%2527s_algorithm/9JwEtznC">Shor's algorithm</a>: provides <a href="/facts/Exponential_function/ewlYxvR2">exponential</a> speedup (relative to currently known non-quantum algorithms) for factoring a number</li> <li><a href="/facts/Simon%2527s_algorithm/t5BKvXCI">Simon's algorithm</a>: provides a provably <a href="/facts/Exponential_function/ewlYxvR2">exponential</a> speedup (relative to any non-quantum algorithm) for a black-box problem</li></ul> <h3>Theory of computation and automata</h3> <p class="note">Further information: <a href="/facts/Theory_of_computation/xYJd2YeI">Theory of computation</a></p> <ul><li><a href="/facts/DFA_minimization/qASLWje9">Hopcroft's algorithm</a>, <a href="/facts/DFA_minimization/qASLWje9">Moore's algorithm</a>, and <a href="/facts/DFA_minimization/qASLWje9">Brzozowski's algorithm</a>: algorithms for <a href="/facts/DFA_minimization/qASLWje9">minimizing the number of states in a deterministic finite automaton</a></li> <li><a href="/facts/Powerset_construction/FeTghmH7">Powerset construction</a>: algorithm to convert nondeterministic automaton to <a href="/facts/Deterministic_automaton/J8duzAfh">deterministic automaton</a>.</li> <li><a href="/facts/Tarski%25E2%2580%2593Kuratowski_algorithm/6cbhHSjr">Tarski–Kuratowski algorithm</a>: a <a href="/facts/Non-deterministic_algorithm/UubLdp3D">non-deterministic algorithm</a> which provides an upper bound for the complexity of formulas in the <a href="/facts/Arithmetical_hierarchy/rQptcBFK">arithmetical hierarchy</a> and <a href="/facts/Analytical_hierarchy/C9r61LzA">analytical hierarchy</a></li></ul> <h2 id="information-theory-and-signal-processing">Information theory and signal processing</h2> <p class="note">Main articles: <a href="/facts/Information_theory/qNLH3U5P">Information theory</a> and <a href="/facts/Signal_processing/Npaja6zb">Signal processing</a></p> <h3>Coding theory</h3> <p class="note">Further information: <a href="/facts/Coding_theory/SBqStoGL">Coding theory</a></p> <h4>Error detection and correction</h4> <p class="note">Further information: <a href="/facts/Error_detection_and_correction/o2rH8e3n">Error detection and correction</a></p> <ul><li><a href="/facts/BCH_Code/1KelJGxF">BCH Codes</a> <ul><li><a href="/facts/Berlekamp%25E2%2580%2593Massey_algorithm/cDwPPkk0">Berlekamp–Massey algorithm</a></li> <li><a href="/facts/Peterson%25E2%2580%2593Gorenstein%25E2%2580%2593Zierler_algorithm/1KelJGxF">Peterson–Gorenstein–Zierler algorithm</a></li> <li><a href="/facts/Reed%25E2%2580%2593Solomon_error_correction/HPc3Qj6N">Reed–Solomon error correction</a></li></ul></li> <li><a href="/facts/BCJR_algorithm/3Gc7zhwj">BCJR algorithm</a>: decoding of error correcting codes defined on trellises (principally convolutional codes)</li> <li><a href="/facts/Forward_error_correction/cLUTUJrA">Forward error correction</a></li> <li><a href="/facts/Gray_code/HtbVlM7T">Gray code</a></li> <li><a href="/facts/Hamming_code/zsI8cTRC">Hamming codes</a> <ul><li><a href="/facts/Hamming(7%2c4)/JKfbJUS1">Hamming(7,4)</a>: a <a href="/facts/Hamming_code/zsI8cTRC">Hamming code</a> that encodes 4 bits of data into 7 bits by adding 3 parity bits</li> <li><a href="/facts/Hamming_distance/MgdtbYPo">Hamming distance</a>: sum number of positions which are different</li> <li><a href="/facts/Hamming_weight/dJIW7qg4">Hamming weight</a> (population count): find the number of 1 bits in a binary word</li></ul></li> <li><a href="/facts/Redundancy_check/o2rH8e3n">Redundancy checks</a> <ul><li><a href="/facts/Adler-32/fcUX7I00">Adler-32</a></li> <li><a href="/facts/Cyclic_redundancy_check/u2exo4sv">Cyclic redundancy check</a></li> <li><a href="/facts/Damm_algorithm/h6YESDL5">Damm algorithm</a></li> <li><a href="/facts/Fletcher%2527s_checksum/Du1EshMG">Fletcher's checksum</a></li> <li><a href="/facts/Longitudinal_redundancy_check/vGoJjpjR">Longitudinal redundancy check</a> (LRC)</li> <li><a href="/facts/Luhn_algorithm/s44Qds5L">Luhn algorithm</a>: a method of validating identification numbers</li> <li><a href="/facts/Luhn_mod_N_algorithm/pAh0FXWA">Luhn mod N algorithm</a>: extension of Luhn to non-numeric characters</li> <li><a href="/facts/Parity_bit/peFp3Wau">Parity</a>: simple/fast error detection technique</li> <li><a href="/facts/Verhoeff_algorithm/AHq7WhQw">Verhoeff algorithm</a></li></ul></li></ul> <h4>Lossless compression algorithms</h4> <p class="note">Main page: Lossless compression algorithms</p> <ul><li><a href="/facts/Burrows%25E2%2580%2593Wheeler_transform/yxIc9E94">Burrows–Wheeler transform</a>: preprocessing useful for improving <a href="/facts/Lossless_data_compression/LS702KsN">lossless compression</a></li> <li><a href="/facts/Context_tree_weighting/NdvBWGs7">Context tree weighting</a></li> <li><a href="/facts/Delta_encoding/2NQlyAUc">Delta encoding</a>: aid to compression of data in which sequential data occurs frequently</li> <li><a href="/facts/Dynamic_Markov_compression/Qt8TVeh2">Dynamic Markov compression</a>: Compression using predictive arithmetic coding</li> <li><a href="/facts/Dictionary_coder/Y0u9Ysz5">Dictionary coders</a> <ul><li><a href="/facts/Byte_pair_encoding/lPvX89xK">Byte pair encoding</a> (BPE)</li> <li><a href="/facts/Deflate/XnBt1GKV">Deflate</a></li> <li><a href="/facts/Abraham_Lempel/689EaYp3">Lempel</a>–<a href="/facts/Jacob_Ziv/GKDe7C9b">Ziv</a> <ul><li><a href="/facts/LZ77_and_LZ78/HGH09JM9">LZ77 and LZ78</a></li> <li><a href="/facts/LZJB/o6q7g1Kv">Lempel–Ziv Jeff Bonwick</a> (LZJB)</li> <li><a href="/facts/Lempel%25E2%2580%2593Ziv%25E2%2580%2593Markov_chain_algorithm/XMBm3MBK">Lempel–Ziv–Markov chain algorithm</a> (LZMA)</li> <li><a href="/facts/Lempel%25E2%2580%2593Ziv%25E2%2580%2593Oberhumer/hfS0lRrD">Lempel–Ziv–Oberhumer</a> (LZO): speed oriented</li> <li><a href="/facts/LZRW/g2kIrN6S">Lempel–Ziv Ross Williams</a> (LZRW)</li> <li><a href="/facts/Lempel%25E2%2580%2593Ziv%25E2%2580%2593Stac/EexMXmjd">Lempel–Ziv–Stac</a> (LZS)</li> <li><a href="/facts/Lempel%25E2%2580%2593Ziv%25E2%2580%2593Storer%25E2%2580%2593Szymanski/KHe7a3eJ">Lempel–Ziv–Storer–Szymanski</a> (LZSS)</li> <li><a href="/facts/Lempel%25E2%2580%2593Ziv%25E2%2580%2593Welch/hJfgYm9j">Lempel–Ziv–Welch</a> (LZW)</li> <li><a href="/facts/LZWL/DaUsHL4P">LZWL</a>: syllable-based variant</li> <li><a href="/facts/LZX/XpUz9NNB">LZX</a></li></ul></li></ul></li> <li><a href="/facts/Entropy_encoding/44I0n8F8">Entropy encoding</a>: coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols <ul><li><a href="/facts/Arithmetic_coding/WU0H4oNu">Arithmetic coding</a>: advanced <a href="/facts/Entropy/s52IXeFz">entropy</a> coding <ul><li><a href="/facts/Range_encoding/36anhArm">Range encoding</a>: same as <a href="/facts/Arithmetic_coding/WU0H4oNu">arithmetic coding</a>, but looked at in a slightly different way</li></ul></li> <li><a href="/facts/Huffman_coding/dBgMBz48">Huffman coding</a>: simple lossless compression taking advantage of relative character frequencies <ul><li><a href="/facts/Adaptive_Huffman_coding/e4uvINGg">Adaptive Huffman coding</a>: <a href="/facts/Adaptive_coding/f12Pl1QG">adaptive coding</a> technique based on Huffman coding</li> <li><a href="/facts/Package-merge_algorithm/2VXwD6XD">Package-merge algorithm</a>: Optimizes Huffman coding subject to a length restriction on code strings</li></ul></li> <li><a href="/facts/Shannon%25E2%2580%2593Fano_coding/6QNppyt9">Shannon–Fano coding</a></li> <li><a href="/facts/Shannon%25E2%2580%2593Fano%25E2%2580%2593Elias_coding/22peHUzg">Shannon–Fano–Elias coding</a>: precursor to arithmetic encoding<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a></li></ul></li> <li><a href="/facts/Entropy_encoding/44I0n8F8">Entropy coding with known entropy characteristics</a> <ul><li><a href="/facts/Golomb_coding/bUyW4uLN">Golomb coding</a>: form of entropy coding that is optimal for alphabets following geometric distributions</li> <li><a href="/facts/Rice_coding/bUyW4uLN">Rice coding</a>: form of entropy coding that is optimal for alphabets following geometric distributions</li> <li><a href="/facts/Truncated_binary_encoding/5wSGS6la">Truncated binary encoding</a></li> <li><a href="/facts/Unary_coding/yHF7r7pE">Unary coding</a>: code that represents a number n with n ones followed by a zero</li> <li><a href="/facts/Universal_code_(data_compression)/9zn1cM2M">Universal codes</a>: encodes positive integers into binary code words <ul><li>Elias <a href="/facts/Elias_delta_coding/LoDaPWqx">delta</a>, <a href="/facts/Elias_gamma_coding/kcNSUnBg">gamma</a>, and <a href="/facts/Elias_omega_coding/uxHF9zyx">omega</a> coding</li> <li><a href="/facts/Exponential-Golomb_coding/gGrYPQCw">Exponential-Golomb coding</a></li> <li><a href="/facts/Fibonacci_coding/GXCLAf7t">Fibonacci coding</a></li> <li><a href="/facts/Levenshtein_coding/ACQLnfgw">Levenshtein coding</a></li></ul></li></ul></li> <li><a href="/facts/FELICS/c3MQQwpV">Fast Efficient & Lossless Image Compression System</a> (FELICS): a lossless image compression algorithm</li> <li><a href="/facts/Incremental_encoding/hu94Vh22">Incremental encoding</a>: delta encoding applied to sequences of strings</li> <li><a href="/facts/PPM_compression_algorithm/cc621LIE">Prediction by partial matching</a> (PPM): an adaptive statistical data compression technique based on context modeling and prediction</li> <li><a href="/facts/Run-length_encoding/3k6x9afM">Run-length encoding</a>: lossless data compression taking advantage of strings of repeated characters</li> <li><a href="/facts/SEQUITUR_algorithm/8KougpNI">SEQUITUR algorithm</a>: lossless compression by incremental grammar inference on a string</li></ul> <h4>Lossy compression algorithms</h4> <p class="note">Main page: Lossy compression algorithms</p> <ul><li><a href="/facts/3Dc/CILfELvg">3Dc</a>: a lossy data compression algorithm for <a href="/facts/Normal_mapping/7YmzxkPp">normal maps</a></li> <li><a href="/facts/Audio_data_compression/gMFuY4FT">Audio</a> and <a href="/facts/Speech_encoding/xs5gvMXq">Speech</a> compression <ul><li><a href="/facts/A-law_algorithm/PI9UC1nc">A-law algorithm</a>: standard companding algorithm</li> <li><a href="/facts/Code-excited_linear_prediction/Shkm4bjo">Code-excited linear prediction</a> (CELP): low bit-rate speech compression</li> <li><a href="/facts/Linear_predictive_coding/2Bl1xdSN">Linear predictive coding</a> (LPC): lossy compression by representing the <a href="/facts/Spectral_envelope/RJL6ajoo">spectral envelope</a> of a digital signal of speech in compressed form</li> <li><a href="/facts/Mu-law_algorithm/Ve8vJ6mb">Mu-law algorithm</a>: standard analog signal compression or companding algorithm</li> <li><a href="/facts/Warped_Linear_Predictive_Coding/xJJA5bg5">Warped Linear Predictive Coding</a> (WLPC)</li></ul></li> <li><a href="/facts/Image_compression/q9bfesUr">Image compression</a> <ul><li><a href="/facts/Block_Truncation_Coding/nbSLhly9">Block Truncation Coding</a> (BTC): a type of lossy image compression technique for greyscale images</li> <li><a href="/facts/Embedded_Zerotree_Wavelet/KPjuEj2y">Embedded Zerotree Wavelet</a> (EZW)</li> <li><a href="/facts/Fast_Cosine_Transform/gPpDhPwP">Fast Cosine Transform algorithms</a> (FCT algorithms): computes Discrete Cosine Transform (DCT) efficiently</li> <li><a href="/facts/Fractal_compression/d2qUg7sc">Fractal compression</a>: method used to compress images using fractals</li> <li><a href="/facts/Set_Partitioning_in_Hierarchical_Trees/vH01yXs1">Set Partitioning in Hierarchical Trees</a> (SPIHT)</li> <li><a href="/facts/Wavelet_compression/4vk3W5be">Wavelet compression</a>: form of data compression well suited for <a href="/facts/Image_compression/q9bfesUr">image compression</a> (sometimes also video compression and audio compression)</li></ul></li> <li><a href="/facts/Transform_coding/JGJISRFW">Transform coding</a>: type of data compression for "natural" data like audio signals or photographic images</li> <li><a href="/facts/Vector_quantization/rKNehCok">Vector quantization</a>: technique often used in lossy data compression</li> <li><a href="/facts/Video_compression/gMFuY4FT">Video compression</a></li></ul> <h3>Digital signal processing</h3> <p class="note">Further information: <a href="/facts/Digital_signal_processing/PEG7azr8">Digital signal processing</a></p> <ul><li><a href="/facts/Adaptive-additive_algorithm/ABTDvM1D">Adaptive-additive algorithm</a> (AA algorithm): find the spatial frequency phase of an observed wave source</li> <li><a href="/facts/Discrete_Fourier_transform/uK9Tjsbl">Discrete Fourier transform</a>: determines the frequencies contained in a (segment of a) signal <ul><li><a href="/facts/Bluestein%2527s_FFT_algorithm/1HDuWH4X">Bluestein's FFT algorithm</a></li> <li><a href="/facts/Bruun%2527s_FFT_algorithm/CYdW2QfS">Bruun's FFT algorithm</a></li> <li><a href="/facts/Cooley%25E2%2580%2593Tukey_FFT_algorithm/03VB7JrC">Cooley–Tukey FFT algorithm</a></li> <li><a href="/facts/Fast_Fourier_transform/caT7UUCh">Fast Fourier transform</a></li> <li><a href="/facts/Prime-factor_FFT_algorithm/LmN9Astb">Prime-factor FFT algorithm</a></li> <li><a href="/facts/Rader%2527s_FFT_algorithm/tuNKtRMC">Rader's FFT algorithm</a></li></ul></li> <li><a href="/facts/Fast_folding_algorithm/8CKGkPrg">Fast folding algorithm</a>: an efficient algorithm for the detection of approximately periodic events within time series data</li> <li><a href="/facts/Gerchberg%25E2%2580%2593Saxton_algorithm/Ghlyj0a2">Gerchberg–Saxton algorithm</a>: Phase retrieval algorithm for optical planes</li> <li><a href="/facts/Goertzel_algorithm/QMrSIQjm">Goertzel algorithm</a>: identify a particular frequency component in a signal. Can be used for <a href="/facts/DTMF/vg5vFo0X">DTMF</a> digit decoding.</li> <li><a href="/facts/Karplus-Strong_string_synthesis/nV3kHJbA">Karplus-Strong string synthesis</a>: physical modelling synthesis to simulate the sound of a hammered or plucked string or some types of percussion</li></ul> <h4>Image processing</h4> <p class="note">Further information: <a href="/facts/Digital_image_processing/zenalNCf">Digital image processing</a></p> <ul><li><a href="/facts/Adaptive_histogram_equalization/U6J871lw">Adaptive histogram equalization</a>: histogram equalization which adapts to local changes in contrast - Contrast Enhancement</li> <li><a href="/facts/Blind_deconvolution/E6mgQQ3a">Blind deconvolution</a>: image de-blurring algorithm when <a href="/facts/Point_spread_function/9cUtf9P0">point spread function</a> is unknown.</li> <li><a href="/facts/Connected-component_labeling/DjFKJxx8">Connected-component labeling</a>: find and label disjoint regions</li> <li><a href="/facts/Dithering/fCBytTzz">Dithering</a> and <a href="/facts/Half-toning/HcLxHwrY">half-toning</a> <ul><li><a href="/facts/Error_diffusion/2YypJEg9">Error diffusion</a></li> <li><a href="/facts/Floyd%25E2%2580%2593Steinberg_dithering/Thqb39o1">Floyd–Steinberg dithering</a></li> <li><a href="/facts/Ordered_dithering/JtHBa5C6">Ordered dithering</a></li> <li><a href="/facts/Riemersma_dithering/fCBytTzz">Riemersma dithering</a></li></ul></li> <li>Elser <a href="/facts/Difference-map_algorithm/nkhgPmWU">difference-map algorithm</a>: a search algorithm for general constraint satisfaction problems. Originally used for <a href="/facts/X-ray_crystallography/WtI0F5DN">X-Ray diffraction</a> microscopy</li> <li><a href="/facts/Feature_detection_(computer_vision)/GdfWRp5U">Feature detection</a> <ul><li><a href="/facts/Canny_edge_detector/z4EExfNu">Canny edge detector</a>: detect a wide range of edges in images</li> <li><a href="/facts/Generalised_Hough_transform/ARs3VIlD">Generalised Hough transform</a></li> <li><a href="/facts/Hough_transform/cYmx4Duw">Hough transform</a></li> <li><a href="/facts/Marr%25E2%2580%2593Hildreth_algorithm/xWys4o6V">Marr–Hildreth algorithm</a>: an early <a href="/facts/Edge_detection/9VplpIcS">edge detection</a> algorithm</li> <li><a href="/facts/Scale-invariant_feature_transform/oX14fcpr">SIFT</a> (Scale-invariant feature transform): is an algorithm to detect and describe local features in images.</li> <li>SURF (<a href="/facts/Speeded_up_robust_features/8yNYo6Kn">Speeded Up Robust Features</a>): is a robust local feature detector, first presented by <a href="/facts/Herbert_Bay/8yNYo6Kn">Herbert Bay</a> et al. in 2006, that can be used in computer vision tasks like object recognition or 3D reconstruction. It is partly inspired by the SIFT descriptor. The standard version of SURF is several times faster than SIFT and claimed by its authors to be more robust against different image transformations than SIFT.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a><a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a></li></ul></li> <li><a href="/facts/Histogram_equalization/vmohr7XK">Histogram equalization</a>: use histogram to improve image contrast - Contrast Enhancement</li> <li><a href="/facts/Richardson%25E2%2580%2593Lucy_deconvolution/6F6YlysH">Richardson–Lucy deconvolution</a>: image de-blurring algorithm</li> <li><a href="/facts/Median_filtering/YU4NdjKT">Median filtering</a></li> <li><a href="/facts/Seam_carving/9cdqm2Xo">Seam carving</a>: content-aware image resizing algorithm</li> <li><a href="/facts/Segmentation_(image_processing)/jofAhbxa">Segmentation</a>: partition a digital image into two or more regions <ul><li><a href="/facts/GrowCut_algorithm/PRp74xQC">GrowCut algorithm</a>: an interactive segmentation algorithm</li> <li><a href="/facts/Random_walker_algorithm/IFo2Ms8r">Random walker algorithm</a></li> <li><a href="/facts/Region_growing/US9D0lYD">Region growing</a></li> <li><a href="/facts/Watershed_(algorithm)/BaTCIB7b">Watershed transformation</a>: a class of algorithms based on the watershed analogy</li></ul></li></ul> <h2 id="software-engineering">Software engineering</h2> <p class="note">Further information: <a href="/facts/Software_engineering/KX6cE9kz">Software engineering</a></p> <ul><li><a href="/facts/Cache_algorithms/LFW5UqPo">Cache algorithms</a></li> <li><a href="/facts/CHS_conversion/WWtvA0E2">CHS conversion</a>: converting between disk addressing systems</li> <li><a href="/facts/Double_dabble/Ns0660RA">Double dabble</a>: convert binary numbers to BCD</li> <li><a href="/facts/Hash_function/rk6MlCt3">Hash function</a>: convert a large, possibly variable-sized amount of data into a small datum, usually a single integer that may serve as an index into an array <ul><li><a href="/facts/Fowler%25E2%2580%2593Noll%25E2%2580%2593Vo_hash_function/C9VHCDmB">Fowler–Noll–Vo hash function</a>: fast with low collision rate</li> <li><a href="/facts/Pearson_hashing/sSyV6TdS">Pearson hashing</a>: computes 8-bit value only, optimized for 8-bit computers</li> <li><a href="/facts/Zobrist_hashing/CTfD0GWd">Zobrist hashing</a>: used in the implementation of <a href="/facts/Transposition_table/KslgQ7sn">transposition tables</a></li></ul></li> <li><a href="/facts/Unicode_collation_algorithm/4VydIteq">Unicode collation algorithm</a></li> <li><a href="/facts/Xor_swap_algorithm/RYvsz6dd">Xor swap algorithm</a>: swaps the values of two variables without using a buffer</li></ul> <h2 id="database-algorithms">Database algorithms</h2> <p class="note">Further information: <a href="/facts/Database/VYcpkevb">Database</a></p> <ul><li><a href="/facts/Algorithms_for_Recovery_and_Isolation_Exploiting_Semantics/KYLGWQQF">Algorithms for Recovery and Isolation Exploiting Semantics</a> (ARIES): <a href="/facts/Transaction_(database)/q1Etrsl8">transaction</a> recovery</li> <li><a href="/facts/Join_(SQL)/Cxl5lxcR">Join algorithms</a> <ul><li><a href="/facts/Block_nested_loop/74nCrNKl">Block nested loop</a></li> <li><a href="/facts/Hash_join/WryEJk9d">Hash join</a></li> <li><a href="/facts/Nested_loop_join/LV246CsC">Nested loop join</a></li> <li><a href="/facts/Sort-Merge_Join/S8NMJ6e7">Sort-Merge Join</a></li></ul></li> <li><a href="/facts/Chase_(algorithm)/JfTgn5nt">The Chase</a></li></ul> <h2 id="distributed-systems-algorithms">Distributed systems algorithms</h2> <p class="note">Further information: <a href="/facts/Distributed_algorithm/S35ydYjK">Distributed algorithm</a> and <a href="/facts/Distributed_systems/o5nyhqTF">Distributed systems</a></p> <ul><li><a href="/facts/Clock_synchronization/xKykfAJ5">Clock synchronization</a> <ul><li><a href="/facts/Berkeley_algorithm/PNpfIVHl">Berkeley algorithm</a></li> <li><a href="/facts/Cristian%2527s_algorithm/BgjoNFKp">Cristian's algorithm</a></li> <li><a href="/facts/Intersection_algorithm/F53zBjMr">Intersection algorithm</a></li> <li><a href="/facts/Marzullo%2527s_algorithm/1f358gMd">Marzullo's algorithm</a></li></ul></li> <li><a href="/facts/Consensus_(computer_science)/rC0eH88V">Consensus (computer science)</a>: agreeing on a single value or history among unreliable processors <ul><li><a href="/facts/Chandra%25E2%2580%2593Toueg_consensus_algorithm/sHmNr4XE">Chandra–Toueg consensus algorithm</a></li> <li><a href="/facts/Paxos_algorithm/S7KYPNb6">Paxos algorithm</a></li> <li><a href="/facts/Raft_(computer_science)/ppsFb4Xq">Raft (computer science)</a></li></ul></li> <li>Detection of Process Termination <ul><li><a href="/facts/Dijkstra-Scholten_algorithm/cRfcT5t8">Dijkstra-Scholten algorithm</a></li> <li><a href="/facts/Huang%2527s_algorithm/EsItMX0n">Huang's algorithm</a></li></ul></li> <li><a href="/facts/Lamport_ordering/I3oA64q3">Lamport ordering</a>: a <a href="/facts/Partial_order/qb4a3FAX">partial ordering</a> of events based on the <i>happened-before</i> relation</li> <li><a href="/facts/Leader_election/Hsc4FGNb">Leader election</a>: a method for dynamically selecting a coordinator <ul><li><a href="/facts/Bully_algorithm/aXVGaH5H">Bully algorithm</a></li></ul></li> <li><a href="/facts/Mutual_exclusion/1dwvCxDW">Mutual exclusion</a> <ul><li><a href="/facts/Lamport%2527s_Distributed_Mutual_Exclusion_Algorithm/TkFhgM33">Lamport's Distributed Mutual Exclusion Algorithm</a></li> <li><a href="/facts/Naimi-Trehel%2527s_log(n)_Algorithm/0NXr8Ime">Naimi-Trehel's log(n) Algorithm</a></li> <li><a href="/facts/Maekawa%2527s_algorithm/oMsm7jML">Maekawa's Algorithm</a></li> <li><a href="/facts/Raymond%2527s_algorithm/zWQ0WpgN">Raymond's Algorithm</a></li> <li><a href="/facts/Ricart%25E2%2580%2593Agrawala_algorithm/hrK9KoVS">Ricart–Agrawala Algorithm</a></li></ul></li> <li><a href="/facts/Snapshot_algorithm/RtBwxIMy">Snapshot algorithm</a>: record a consistent global state for an asynchronous system <ul><li><a href="/facts/Chandy%25E2%2580%2593Lamport_algorithm/KsNJ5nYQ">Chandy–Lamport algorithm</a></li></ul></li> <li><a href="/facts/Vector_clocks/IW3DwGFV">Vector clocks</a>: generate a <a href="/facts/Partial_ordering/qb4a3FAX">partial ordering</a> of events in a distributed system and detect <a href="/facts/Causality/Swh496X7">causality</a> violations</li></ul> <h3>Memory allocation and deallocation algorithms</h3> <ul><li><a href="/facts/Buddy_memory_allocation/nTr3e7A4">Buddy memory allocation</a>: an algorithm to allocate memory such with less fragmentation</li> <li><a href="/facts/Garbage_collection_(computer_science)/j2vlIu7g">Garbage collectors</a> <ul><li><a href="/facts/Cheney%2527s_algorithm/os1f0IpL">Cheney's algorithm</a>: an improvement on the Semi-space collector</li> <li><a href="/facts/Garbage_collection_(computer_science)/j2vlIu7g">Generational garbage collector</a>: Fast garbage collectors that segregate memory by age</li> <li><a href="/facts/Mark-compact_algorithm/NwHFdoY5">Mark-compact algorithm</a>: a combination of the <a href="/facts/Mark_and_sweep/qg7fK6w9">mark-sweep algorithm</a> and <a href="/facts/Cheney%2527s_algorithm/os1f0IpL">Cheney's copying algorithm</a></li> <li><a href="/facts/Mark_and_sweep/qg7fK6w9">Mark and sweep</a></li> <li>Semi-space collector: an early copying collector</li></ul></li> <li><a href="/facts/Reference_counting/jbPcXuXe">Reference counting</a></li></ul> <h2 id="networking">Networking</h2> <p class="note">Further information: <a href="/facts/Network_scheduler/7URA71LE">Network scheduler</a></p> <ul><li><a href="/facts/Karn%2527s_algorithm/WvJxAcjv">Karn's algorithm</a>: addresses the problem of getting accurate estimates of the round-trip time for messages when using TCP</li> <li><a href="/facts/Lule%25C3%25A5_algorithm/TUz9lPcw">Luleå algorithm</a>: a technique for storing and searching internet routing tables efficiently</li> <li><a href="/facts/Network_congestion/9ohkRMso">Network congestion</a> <ul><li><a href="/facts/Exponential_backoff/pk2cAbqm">Exponential backoff</a></li> <li><a href="/facts/Nagle%2527s_algorithm/s0gpGezx">Nagle's algorithm</a>: improve the efficiency of TCP/IP networks by coalescing packets</li> <li><a href="/facts/Truncated_binary_exponential_backoff/pk2cAbqm">Truncated binary exponential backoff</a></li></ul></li></ul> <h2 id="operating-systems-algorithms">Operating systems algorithms</h2> <p class="note">Further information: <a href="/facts/Operating_systems/8XTuvMh2">Operating systems</a></p> <ul><li><a href="/facts/Banker%2527s_algorithm/59Ps5YXI">Banker's algorithm</a>: algorithm used for deadlock avoidance</li> <li><a href="/facts/Page_replacement_algorithms/ApuSJLaq">Page replacement algorithms</a>: for selecting the victim page under low memory conditions <ul><li><a href="/facts/Adaptive_replacement_cache/KqUfMduG">Adaptive replacement cache</a>: better performance than LRU</li> <li><a href="/facts/Clock_with_Adaptive_Replacement/ApuSJLaq">Clock with Adaptive Replacement</a> (CAR): a page replacement algorithm with performance comparable to <a href="/facts/Adaptive_replacement_cache/KqUfMduG">adaptive replacement cache</a></li></ul></li></ul> <h3>Process synchronization</h3> <p class="note">Further information: <a href="/facts/Process_scheduler/XptmcM1a">Process scheduler</a> and <a href="/facts/Process_synchronization/n7ID76uM">Process synchronization</a></p> <ul><li><a href="/facts/Dekker%2527s_algorithm/xfRMh5hI">Dekker's algorithm</a></li> <li><a href="/facts/Lamport%2527s_Bakery_algorithm/LhNIQ02p">Lamport's Bakery algorithm</a></li> <li><a href="/facts/Peterson%2527s_algorithm/DU3jLWsk">Peterson's algorithm</a></li></ul> <h3>Scheduling</h3> <p class="note">Further information: <a href="/facts/Scheduling_(computing)/XptmcM1a">Scheduling (computing)</a></p> <ul><li><a href="/facts/Earliest_deadline_first_scheduling/goPSVuAQ">Earliest deadline first scheduling</a></li> <li><a href="/facts/Fair-share_scheduling/8jqDbFL3">Fair-share scheduling</a></li> <li><a href="/facts/Least_slack_time_scheduling/tVe4XVkQ">Least slack time scheduling</a></li> <li><a href="/facts/List_scheduling/qUscTqbx">List scheduling</a></li> <li><a href="/facts/Multi_level_feedback_queue/3RxJDMXp">Multi level feedback queue</a></li> <li><a href="/facts/Rate-monotonic_scheduling/o6RXz064">Rate-monotonic scheduling</a></li> <li><a href="/facts/Round-robin_scheduling/7wpjbMRI">Round-robin scheduling</a></li> <li><a href="/facts/Shortest_job_next/FUePWk84">Shortest job next</a></li> <li><a href="/facts/Shortest_remaining_time/8Po1dy9U">Shortest remaining time</a></li> <li><a href="/facts/Top-nodes_algorithm/GNhFKxqK">Top-nodes algorithm</a>: resource calendar management</li></ul> <h3>I/O scheduling</h3> <p class="note">Further information: <a href="/facts/I%2fO_scheduling/4WvHrePc">I/O scheduling</a></p> <h4>Disk scheduling</h4> <ul><li><a href="/facts/Elevator_algorithm/taDJA0A5">Elevator algorithm</a>: Disk scheduling algorithm that works like an elevator.</li> <li><a href="/facts/Shortest_seek_first/BW2VzBpl">Shortest seek first</a>: Disk scheduling algorithm to reduce <a href="/facts/Seek_time/leXXc5qd">seek time</a>.</li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/List_of_data_structures/25H7hEPa">List of data structures</a></li> <li><a href="/facts/List_of_machine_learning_algorithms/0Vxx79yj">List of machine learning algorithms</a></li> <li><a href="/facts/List_of_pathfinding_algorithms/x9Ho1cvp">List of pathfinding algorithms</a></li> <li><a href="/facts/List_of_algorithm_general_topics/n5Nzyx63">List of algorithm general topics</a></li> <li><a href="/facts/List_of_terms_relating_to_algorithms_and_data_structures/9jCn2VVA">List of terms relating to algorithms and data structures</a></li> <li><a href="/facts/Heuristic/BcBEkv9c">Heuristic</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>"algorithm". LII / Legal Information Institute. Retrieved 2023-10-26. <a href="https://www.law.cornell.edu/wex/algorithm" target="_blank">https://www.law.cornell.edu/wex/algorithm</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Gegenfurtner, Karl R. (1992-12-01). "PRAXIS: Brent's algorithm for function minimization". Behavior Research Methods, Instruments, & Computers. 24 (4): 560–564. doi:10.3758/BF03203605. ISSN 1532-5970. <a href="https://doi.org/10.3758%2FBF03203605" target="_blank">https://doi.org/10.3758%2FBF03203605</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>"richardshin.com | Floyd's Cycle Detection Algorithm". 2013-09-30. Retrieved 2023-10-26. <a href="http://www.richardshin.com/floyds-cycle-detection-algorithm/" target="_blank">http://www.richardshin.com/floyds-cycle-detection-algorithm/</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Tesler, G. (2020). "Ch. 5.9: Gale-Shapley Algorithm" (PDF). mathweb.ucsd.edu. University of California San Diego. Retrieved 26 April 2025. <a href="https://mathweb.ucsd.edu/~gptesler/154/slides/154_galeshapley_20-handout.pdf" target="_blank">https://mathweb.ucsd.edu/~gptesler/154/slides/154_galeshapley_20-handout.pdf</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Kleinberg, Jon; Tardos, Éva (2005). "Algorithmn Design: 1. Stable Matching" (PDF). www.cs.princeton.edu. Pearson-Addison Wesley: Princeton University. Retrieved 26 April 2025. <a href="https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/01StableMatching.pdf" target="_blank">https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pdf/01StableMatching.pdf</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Goel, Ashish (21 January 2019). Ramseyer, Geo (ed.). "CS261 Winter 2018- 2019 Lecture 5: Gale-Shapley Algorith" (PDF). web.stanford.edu. Stanford University. Retrieved 26 April 2025. <a href="https://web.stanford.edu/~ashishg/cs261/win21/notes/l5_note.pdf" target="_blank">https://web.stanford.edu/~ashishg/cs261/win21/notes/l5_note.pdf</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>"Eytzinger Binary Search - Algorithmica". Retrieved 2023-04-09. <a href="https://algorithmica.org/en/eytzinger" target="_blank">https://algorithmica.org/en/eytzinger</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>"A "Sorting" algorithm". Code Golf Stack Exchange. October 30, 2018. Retrieved April 4, 2025. <a href="https://codegolf.stackexchange.com/questions/174964/a-sorting-algorithm" target="_blank">https://codegolf.stackexchange.com/questions/174964/a-sorting-algorithm</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>"Shannon-Fano-Elias Coding" (PDF). my.ece.msstate.edu. Archived from the original (PDF) on 2021-02-28. 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