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Efficient Algorithms for Computing the Triplet and Quartet Distance Between Trees of Arbitrary Degree

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  • Soda13

    Accepted manuscript, 421 KB, PDF document


The triplet and quartet distances are distance measures to compare two rooted and two unrooted trees, respectively. The leaves of the two trees should have the same set of n labels. The distances are defined by enumerating all subsets of three labels (triplets) and four labels (quartets), respectively, and counting how often the induced topologies in the two input trees are different. In this paper we present efficient algorithms for computing these distances. We show how to compute the triplet distance in time O(n log n) and the quartet distance in time O(d n log n), where d is the maximal degree of any node in the two trees. Within the same time bounds, our framework also allows us to compute the parameterized triplet and quartet distances, where a parameter is introduced to weight resolved (binary) topologies against unresolved (non-binary) topologies. The previous best algorithm for computing the triplet and parameterized triplet distances have O(n2) running time, while the previous best algorithms for computing the quartet distance include an O(d9 n log n) time algorithm and an O(n2.688) time algorithm, where the latter can also compute the parameterized quartet distance. Since d ≤ n, our algorithms improve on all these algorithms
Original languageEnglish
JournalThe Annual A C M - S I A M Symposium on Discrete Algorithms. Proceedings
Pages (from-to)1814-1832
Number of pages19
Publication statusPublished - 2013
EventACM-SIAM Symposium on Discrete Algorithms - New Orleans, United States
Duration: 6 Jan 20138 Jan 2013
Conference number: 24


ConferenceACM-SIAM Symposium on Discrete Algorithms
CountryUnited States
CityNew Orleans

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