Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
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
Convex recolorings of strings and trees: Definitions, hardness results and algorithms
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
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
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 complexity of minimum convex coloring
Discrete Applied Mathematics
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A coloring of a graph is convex if the vertices that pertain to any color induce a connected subgraph; a partial coloring (which assigns colors to a subset of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring has applications in fields such as phylogenetics, communication or transportation networks, etc. When a coloring of a graph is not convex, a natural question is how far it is from a convex one. This problem is denoted as convex recoloring (CR). While the initial works on CR defined and studied the problem on trees, recent efforts aim at either generalizing the underlying graphs or specializing the input colorings. In this work, we extend the underlying graph and the input coloring to partially colored galled networks. We show that although determining whether a coloring is convex on an arbitrary network is hard, it can be found efficiently on galled networks. We present a fixed parameter tractable algorithm that finds the recoloring distance of such a network whose running time is quadratic in the network size and exponential in that distance. This complexity is achieved by amortized analysis that uses a novel technique for contracting colored graphs that seems to be of independent interest.