TY - GEN

T1 - Improved approximation algorithm for convex recoloring of trees

AU - Bar-Yehuda, Reuven

AU - Feldman, Ido

AU - Rawitz, Dror

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33745629640&partnerID=8YFLogxK

U2 - 10.1007/11671411_5

DO - 10.1007/11671411_5

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AN - SCOPUS:33745629640

SN - 3540322078

SN - 9783540322078

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 55

EP - 68

BT - Approximation and Online Algorithms - Third International Workshop, WAOA 2005, Revised Selected Papers

T2 - 3rd International Workshop on Approximation and Online Algorithms, WAOA 2005

Y2 - 6 October 2005 through 7 October 2005

ER -