Inferring Evolutionary History from DNA Sequences
SIAM Journal on Computing
Minimizing phylogenetic number to find good evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
A Fast Algorithm for the Computation and Enumeration of Perfect Phylogenies
SIAM Journal on Computing
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Two Strikes Against Perfect Phylogeny
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
On Generating the N-ary Reflected Gray Codes
IEEE Transactions on Computers
Efficient approximation of convex recolorings
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Convex recolorings of strings and trees: definitions, hardness results and algorithms
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Partial convex recolorings of trees and galled networks: Tight upper and lower bounds
ACM Transactions on Algorithms (TALG)
The complexity of minimum convex coloring
Discrete Applied Mathematics
Connected coloring completion for general graphs: algorithms and complexity
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Quadratic kernelization for convex recoloring of trees
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Discrete Applied Mathematics
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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 phylogeny. 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)2 41/ε). This result improves the previously known 3-approximation algorithm for this NP-hard problem.