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
Selecting the branches for an evolutionary tree: a polynomial time approximation scheme
Journal of Algorithms
Parameterized Complexity
Combinatorial optimization in system configuration design
Automation and Remote Control
Convex Recoloring Revisited: Complexity and Exact Algorithms
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
A Kernel for Convex Recoloring of Weighted Forests
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Testing convexity properties of tree colorings
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Speeding up dynamic programming for some NP-hard graph recoloring problems
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
The parameterized complexity of some minimum label problems
Journal of Computer and System Sciences
Partial convex recolorings of trees and galled networks: Tight upper and lower bounds
ACM Transactions on Algorithms (TALG)
Using semi-definite programming to enhance supertree resolvability
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
The complexity of minimum convex coloring
Discrete Applied Mathematics
Discrete Applied Mathematics
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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 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 colored string (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 first generalization is the uniform weighted model, where each vertex has a weight which is the cost of changing its color. The other is the non-uniform model, in which the cost of coloring a vertex v by a color d is an arbitrary non-negative number cost(v,d). Our first algorithms find optimal convex recolorings of strings and bounded degree trees under the non-uniform model in time which, for any fixed number of colors, is linear in the input size. Next we improve these algorithm for the uniform model to run in time which is linear in the input size for a fixed number of bad colors, which are colors which violate convexity in some natural sense. Finally, we generalize the above result to hold for trees of unbounded degree.