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Top tree
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<p>A top tree is a <a href="/facts/Data_structure/yNsNvL1I">data structure</a> based on a binary tree for unrooted dynamic <a href="/facts/Tree_(data_structure)/RcXz9noF">trees</a> that is used mainly for various path-related operations. It allows simple <a href="/facts/Divide-and-conquer_algorithm/pC1X7Ws7">divide-and-conquer algorithms</a>. It has since been augmented to maintain dynamically various properties of a <a href="/facts/Tree_(data_structure)/RcXz9noF">tree</a> such as diameter, center and median. </p><p>A top tree ℜ {\displaystyle \Re } is defined for an <i>underlying tree</i> T and a set ∂ T {\displaystyle \partial {T}} of at most two vertices called as External Boundary Vertices </p>