{"doi":"10.1007/pl00009268","date_created":"2022-07-27T15:02:28Z","publication_status":"published","_id":"11679","publication":"Algorithmica","author":[{"first_name":"Monika H","last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"full_name":"King, V.","last_name":"King","first_name":"V."},{"first_name":"T.","last_name":"Warnow","full_name":"Warnow, T."}],"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"citation":{"mla":"Henzinger, Monika H., 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>.","short":"M.H. Henzinger, V. King, T. Warnow, Algorithmica 24 (1999) 1–13.","ista":"Henzinger MH, King V, Warnow T. 1999. Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. Algorithmica. 24, 1–13.","apa":"Henzinger, M. H., 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>","chicago":"Henzinger, Monika H, 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>.","ieee":"M. H. 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.","ama":"Henzinger MH, 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>"},"publisher":"Springer Nature","scopus_import":"1","related_material":{"record":[{"id":"11927","relation":"earlier_version","status":"public"}]},"date_published":"1999-05-01T00:00:00Z","title":"Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology","type":"journal_article","date_updated":"2023-02-21T16:33:24Z","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["Algorithms","Data structures","Evolutionary biology","Theory of databases"],"quality_controlled":"1","article_type":"original","status":"public","year":"1999","month":"05","intvolume":"        24","article_processing_charge":"No","oa_version":"None","abstract":[{"text":"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 .\r\n\r\nWe 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.","lang":"eng"}],"volume":24,"extern":"1","page":"1-13","language":[{"iso":"eng"}]}