Inferring Evolutionary History from DNA Sequences
SIAM Journal on Computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
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
Class discovery in gene expression data
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Non-Deterministic Polynomial Optimization Problems and Their Approximation
Proceedings of the Fourth Colloquium on Automata, Languages and Programming
Two Strikes Against Perfect Phylogeny
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
A Polynomial-Time Algorithm for Near-Perfect Phylogeny
SIAM Journal on Computing
Improved approximation algorithm for convex recoloring of trees
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Quadratic kernelization for convex recoloring of trees
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arises in areas such as phylogenetics, linguistics, etc. e.g., a perfect phylogenetic tree is one in which the states of each character induce a convex coloring of the tree. Research on perfect phylogeny is usually focused on finding a tree so that few predetermined partial colorings of its vertices are convex. When a coloring of a tree is not convex, it is desirable to know “how far” it is from a convex one. In [MS05], a natural measure for this distance, called the recoloring distance was defined: the minimal number of color changes at the vertices needed to make the coloring convex. This can be viewed as minimizing the number of “exceptional vertices” w.r.t. to a closest convex coloring. The problem was proved to be NP-hard even for colored strings. In this paper we continue the work of [MS05], and present a 2-approximation algorithm of convex recoloring of strings whose running time O(cn), where c is the number of colors and n is the size of the input, and an O(cn2) 3-approximation algorithm for convex recoloring of trees.