On the complexity of solving or approximating convex recoloring problems

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Abstract

Given a graph with an arbitrary vertex coloring, the Convex Recoloring Problem (CR) consists of recoloring the minimum number of vertices so that each color induces a connected subgraph. We focus on the complexity and inapproximabiliy of this problem on k-colored graphs, for fixed k ≥ 2. We prove a very strong complexity result showing that CR is already NP-hard on k-colored grids, and therefore also on planar graphs with maximum degree 4. For each k ≥ 2, we also prove that, for a positive constant c, there is no cln n-approximation algorithm even for k-colored n-vertex bipartite graphs, unless P = NP. For 2-colored (q,q-4)-graphs, a class that includes cographs and P 4-sparse graphs, we present polynomial-time algorithms for fixed q. The same complexity results are obtained for a relaxation of CR, where only one fixed color is required to induce a connected subgraph. © 2013 Springer-Verlag Berlin Heidelberg.

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APA

Campêlo, M. B., Huiban, C. G., Sampaio, R. M., & Wakabayashi, Y. (2013). On the complexity of solving or approximating convex recoloring problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7936 LNCS, pp. 614–625). https://doi.org/10.1007/978-3-642-38768-5_54

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