Fixed parameter tractability of binary near-perfect phylogenetic tree reconstruction

Guy E. Blelloch, Kedar Dhamdhere, Eran Halperin, R. Ravi, Russell Schwartz, Srinath Sridhar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider the problem of finding a Steiner minimum tree in a hypercube. Specifically, given n terminal vertices in an m dimensional cube and a parameter q, we compute the Steiner minimum tree in time O(72q + 8 qnm2), under the assumption that the length of the minimum Steiner tree is at most m + q. This problem has extensive applications in taxonomy and biology. The Steiner tree problem in hypercubes is equivalent to the phylogeny (evolutionary tree) reconstruction problem under the maximum parsimony criterion, when each taxon is defined over binary states. The taxa, character set and mutation of a phylogeny correspond to terminal vertices, dimensions and traversal of a dimension in a Steiner tree. Phylogenetic trees that mutate each character exactly once are called perfect phylogenies and their size is bounded by the number of characters. When a perfect phylogeny consistent with the data set exists it can be constructed in linear time. However, real data sets often do not admit perfect phylogenies. In this paper, we consider the problem of reconstructing near-perfect phylogenetic trees (referred to as BNPP). A near-perfect phylogeny relaxes the perfect phylogeny assumption by allowing at most q additional mutations. We show for the first time that the BNPP problem is fixed parameter tractable (FPT) and significantly improve the previous asymptotic bounds.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 33rd International Colloquium, ICALP 2006, Proceedings
PublisherSpringer Verlag
Pages667-678
Number of pages12
ISBN (Print)3540359044, 9783540359043
DOIs
StatePublished - 2006
Externally publishedYes
Event33rd International Colloquium on Automata, Languages and Programming, ICALP 2006 - Venice, Italy
Duration: 10 Jul 200614 Jul 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4051 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference33rd International Colloquium on Automata, Languages and Programming, ICALP 2006
Country/TerritoryItaly
CityVenice
Period10/07/0614/07/06

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