A linear time approximation scheme for maximum quartet consistency on sparse sampled inputs

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Abstract

Phylogenetic tree reconstruction is a fundamental biological problem. Quartet amalgamation - combining a set of trees over four taxa into a tree over the full set - stands at the heart of many phylogenetic reconstruction methods. However, even reconstruction from a consistent set of quartet trees, i.e. all quartets agree with some tree, is NP-hard, and the best approximation ratio known is 1/3. For a dense input of Θ(n4) quartets (not necessarily consistent), the problem has a polynomial time approximation scheme. When the number of taxa grows, considering such dense inputs is impractical and some sampling approach is imperative. In this paper we show that if the number of quartets sampled is at least Θ(n2 log n), there is a randomized approximation scheme, that runs in linear time in the number of quartets. The previously known polynomial approximation scheme for that problem required a very dense sample of size Θ(n4). We note that samples of size Θ(n2 log n) are sparse in the full quartet set.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings
Pages339-350
Number of pages12
DOIs
StatePublished - 2011
Event14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011 - Princeton, NJ, United States
Duration: 17 Aug 201119 Aug 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6845 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011
Country/TerritoryUnited States
CityPrinceton, NJ
Period17/08/1119/08/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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