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
Class discovery in gene expression data
RECOMB '01 Proceedings of the fifth annual international conference on Computational biology
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
Parameterized Complexity
A 2O (k)poly(n) algorithm for the parameterized Convex Recoloring problem
Information Processing Letters
Efficient approximation of convex recolorings
Journal of Computer and System Sciences
Upper and lower bounds for finding connected motifs in vertex-colored graphs
Journal of Computer and System Sciences
Improved approximation algorithm for convex recoloring of trees
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Sharp tractability borderlines for finding connected motifs in vertex-colored graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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
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A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree. Convex colorings of trees arise 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. When a coloring of a tree is not convex, it is desirable to know ”how far” it is from a convex one, and what are the convex colorings which are ”closest” to it. In this paper we study a natural definition of this distance – the recoloring distance, which is the minimal number of color changes at the vertices needed to make the coloring convex. We show that finding this distance is NP-hard even for a path, and for some other interesting variants of the problem. In the positive side, we present algorithms for computing the recoloring distance under some natural generalizations of this concept: the uniform weighted model and the non-uniform model. Our first algorithms find optimal convex recolorings of strings and bounded degree trees under the non-uniform model in linear time for any fixed number of colors. Next we improve these algorithms for the uniform model to run in linear time for any fixed number of bad colors. Finally, we generalize the above result to hold for trees of unbounded degree.