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
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
Convex recolorings of strings and trees: definitions, hardness results and algorithms
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Connection Matrices for MSOL-Definable Structural Invariants
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
Combinatorial optimization in system configuration design
Automation and Remote Control
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
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
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
Discrete Applied Mathematics
Hi-index | 0.00 |
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 [S. Moran, S. Snir, Convex recoloring of strings and trees: Definitions, hardness results and algorithms, in: WADS, 2005, pp. 218-232; J. Comput. System Sci., submitted for publication], 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. a closest convex coloring. The problem was proved to be NP-hard even for colored strings. In this paper we continue the work of [S. Moran, S. Snir, Convex recoloring of strings and trees: Definitions, hardness results and algorithms, in: WADS, 2005, pp. 218-232; J. Comput. System Sci., submitted for publication], 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(cn^2) 3-approximation algorithm for convex recoloring of trees.