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Maximum Agreement and Compatible Supertrees

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Combinatorial Pattern Matching (CPM 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3109))

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Abstract

Given a collection of trees on n leaves with identical leaf set, the Mast, resp. Mct, problem consists in finding a largest subset of leaves such that all input trees restricted to these leaves are isomorphic, resp. have a common refinement. For Mast, resp. Mct, on k rooted trees, we give an O(min{3p kn,2.27p+kn 3}) exact algorithm, where p is the smallest number of leaves to remove from input trees in order for these trees to be isomorphic, resp. to admit a common refinement. This improves on [14] for Mast and proves fixed-parameter tractability for Mct. We also give an approximation algorithm for (the complement of) Mast similar to the one in [2], but with a better ratio and running time, and extend it to Mct.

We generalize Mast and Mct to the case of supertrees where input trees can have non-identical leaf sets. For the resulting problems, Smast and Smct, we give an O(N+n) time algorithm for the special case of two input trees (N is the time bound for solving Mast, resp. Mct, on two O(n)-leaf trees). Last, we show that Smast and Smct parameterized in p are W[2]-hard and cannot be approximated in polynomial time within a constant factor unless P=NP, even when the input trees are rooted triples.

We also extend the above results to the case of unrooted input trees.

Supported by the Action Incitative Informatique-Mathématique-Physique en Biologie Molé culaire [ACI IMP-Bio].

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Authors and Affiliations

  1. Équipe Méthodes et Algorithmes pour la Bioinformatique – L.I.R.M.M,  

    Vincent Berry & François Nicolas

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  1. Vincent Berry
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  2. François Nicolas
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Editors and Affiliations

  1. School of Computing Science, Simon Fraser University, 8888 University Drive, V5A 1S6, Burnaby, BC, Canada

    Suleyman Cenk Sahinalp

  2. Google Inc., 76 9th Av, 4th Fl., 10011, New York, NY

    S. Muthukrishnan

  3. Tom Sawyer Software, 94612, Oakland, CA, USA

    Ugur Dogrusoz

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Berry, V., Nicolas, F. (2004). Maximum Agreement and Compatible Supertrees. In: Sahinalp, S.C., Muthukrishnan, S., Dogrusoz, U. (eds) Combinatorial Pattern Matching. CPM 2004. Lecture Notes in Computer Science, vol 3109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27801-6_15

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  • DOI: https://doi.org/10.1007/978-3-540-27801-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22341-2

  • Online ISBN: 978-3-540-27801-6

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