Improved approximation algorithm for convex recoloring of trees

Reuven Bar-Yehuda, Ido Feldman, Dror Rawitz

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

6 Scopus citations


A pair (T, C) of a tree T and a coloring C is called a colored tree. Given a colored tree (T, C) any coloring C′ of T is called a recoloring of T. Given a weight function on the vertices of the tree the recoloring distance of a recoloring is the total weight of recolored vertices. A coloring of a tree is convex if for any two vertices u and v that are colored by the same color c, every vertex on the path from u to v is also colored by c. In the minimum convex recoloring problem we are given a colored tree and a weight function and our goal is to find a convex recoloring of minimum recoloring distance. The minimum convex recoloring problem naturally arises in the context of phylogenetic trees. Given a set of related species the goal of phylogenetic reconstruction is to construct a tree that would best describe the evolution of this set of species. In this context a convex coloring correspond to perfect phytogeny. Since perfect phylogeny is not always possible the next best thing is to find a tree which is as close to convex as possible, or, in other words, a tree with minimum recoloring distance. We present a (2+ε)-approximation algorithm for the minimum convex recoloring problem, whose running time is O(n2 + n(1/ε)241/ε). This result improves the previously known 3-approximation algorithm for this NP-hard problem.

Original languageEnglish
Title of host publicationApproximation and Online Algorithms - Third International Workshop, WAOA 2005, Revised Selected Papers
Number of pages14
StatePublished - 2006
Externally publishedYes
Event3rd International Workshop on Approximation and Online Algorithms, WAOA 2005 - Palma de Mallorca, Spain
Duration: 6 Oct 20057 Oct 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3879 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd International Workshop on Approximation and Online Algorithms, WAOA 2005
CityPalma de Mallorca


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