article published yes Monika H Henzinger author 540c9bbd-f2de-11ec-812d-d04a5be856300000-0002-5008-6530 V. King author T. Warnow author We are given a set T = {T 1 ,T 2 , . . .,T k } of rooted binary trees, each T i leaf-labeled by a subset L(Ti)⊂{1,2,...,n} . If T is a tree on {1,2, . . .,n }, we let T|L denote the minimal subtree of T induced by the nodes of L and all their ancestors. The consensus tree problem asks whether there exists a tree T * such that, for every i , T∗|L(Ti) is homeomorphic to T i . We present algorithms which test if a given set of trees has a consensus tree and if so, construct one. The deterministic algorithm takes time min{O(N n 1/2 ), O(N+ n 2 log n )}, where N=∑i|Ti| , and uses linear space. The randomized algorithm takes time O(N log3 n) and uses linear space. The previous best for this problem was a 1981 O(Nn) algorithm by Aho et al. Our faster deterministic algorithm uses a new efficient algorithm for the following interesting dynamic graph problem: Given a graph G with n nodes and m edges and a sequence of b batches of one or more edge deletions, then, after each batch, either find a new component that has just been created or determine that there is no such component. For this problem, we have a simple algorithm with running time O(n 2 log n + b 0 min{n 2 , m log n }), where b 0 is the number of batches which do not result in a new component. For our particular application, b0≤1 . If all edges are deleted, then the best previously known deterministic algorithm requires time O(mn−−√) to solve this problem. We also present two applications of these consensus tree algorithms which solve other problems in computational evolutionary biology. Springer Nature1999 eng AlgorithmsData structuresEvolutionary biologyTheory of databases 0178-4617 1432-054110.1007/pl00009268 241-13 https://research-explorer.ista.ac.at/record/11927 yes Henzinger, Monika, et al. “Constructing a Tree from Homeomorphic Subtrees, with Applications to Computational Evolutionary Biology.” <i>Algorithmica</i>, vol. 24, Springer Nature, 1999, pp. 1–13, doi:<a href="https://doi.org/10.1007/pl00009268">10.1007/pl00009268</a>. Henzinger, Monika, V. King, and T. Warnow. “Constructing a Tree from Homeomorphic Subtrees, with Applications to Computational Evolutionary Biology.” <i>Algorithmica</i>. Springer Nature, 1999. <a href="https://doi.org/10.1007/pl00009268">https://doi.org/10.1007/pl00009268</a>. M. Henzinger, V. King, T. Warnow, Algorithmica 24 (1999) 1–13. Henzinger M, King V, Warnow T. 1999. Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. Algorithmica. 24, 1–13. Henzinger M, King V, Warnow T. Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. <i>Algorithmica</i>. 1999;24:1-13. doi:<a href="https://doi.org/10.1007/pl00009268">10.1007/pl00009268</a> M. Henzinger, V. King, and T. Warnow, “Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology,” <i>Algorithmica</i>, vol. 24. Springer Nature, pp. 1–13, 1999. Henzinger, M., King, V., &#38; Warnow, T. (1999). Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. <i>Algorithmica</i>. Springer Nature. <a href="https://doi.org/10.1007/pl00009268">https://doi.org/10.1007/pl00009268</a> 116792022-07-27T15:02:28Z2024-11-04T11:41:23Z