Hardness and inapproximability of convex recoloring problems

Campêlo, Manoel; Huiban, Cristiana G.; Sampaio, Rudini Menezes; Wakabayashi, Yoshiko

doi:10.1016/j.tcs.2014.03.017

Cited by 8 publications

(2 citation statements)

References 14 publications

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“…Kanj and Kratsch [Kanj and Kratsch 2009] proved that this problem is NP-hard for paths even if each color appears at most twice. Campêlo et al [Campêlo et al 2014] showed that the unweighted CR problem is NP-hard on 2-colored grids. Very recently, Bar-Yehuda et al [Bar-Yehuda et al 2016] designed a 3/2-approximation algorithm for general graphs in which each color appears at most twice.…”

Section: Convex Recoloringmentioning

confidence: 99%

Graph colorings and digraph subdivisions

Moura¹,

Wakabayashi²

2018

Anais Do Concurso De Teses E Dissertações Da SBC (CTD-SBC)

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This paper presents our studies on three vertex coloring problems on graphs and on a problem concerning subdivision of digraphs. Given an arbitrarily colored graph G, the convex recoloring problem consists in finding a (re)coloring that minimizes the number of color changes and such that each color class induces a connected subgraph of G. This problem is motivated by its application in the study of phylogenetic trees in Bioinformatics. In the kfold coloring problem one wishes to cover the vertices of a graph by a minimum number of stable sets in such a way that every vertex is covered by at least k (possibly identical) sets. The proper orientation problem consists in orienting the edges of a graph so that adjacent vertices have different in-degrees and the maximum in-degree is minimized. Our contributions in these problems are in terms of algorithms, hardness, and polyhedral studies. Finally, we investigate a long-standing conjecture of Mader on subdivision of digraphs: for every acyclic digraph H, there exists an integer f (H) such that every digraph with minimum out-degree at least f (H) contains a subdivision of H as a subdigraph. We give evidences for this conjecture by proving it holds for classes of acyclic digraphs.

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Section: Convex Recoloringmentioning

confidence: 99%

Graph colorings and digraph subdivisions

Moura¹,

Wakabayashi²

2018

Anais Do Concurso De Teses E Dissertações Da SBC (CTD-SBC)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Kanj and Kratsch [9] proved that the problem is NP-hard for paths even if each color appears at most twice. Campêlo et al [3] showed that the CR problem is NP-hard on unweighted 2-colored grids. Approximation algorithms for the unweighted case have also been designed: with ratio (2 + ε) for bounded treewidth graphs [8], and ratio 2 for paths [11].…”

Section: Introductionmentioning

confidence: 99%