Weighted Node Coloring: When Stable Sets Are Expensive

Demange, Marc; Werra, Dominique de; Monnot, Jérôme; Paschos, Vangélis Th.

doi:10.1007/3-540-36379-3_11

Cited by 31 publications

(59 citation statements)

References 11 publications

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“…As proved in [4], this problem is approximable in such graphs within approximation ratio 4/3; in the same paper a lower bound of 8/7 − ε, for any ε > 0, was also provided. Here we improve the approximation ratio of [4] by matching the 8/7-lower bound of [4] with a same upper bound; in other words, we show here that min weighted node coloring in bipartite graphs is approximable within approximation ratio bounded above by 8/7.…”

Section: Introductionmentioning

confidence: 73%

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Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation

Werra

Demange

Escoffier

et al. 2004

Algorithms and Computation

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Abstract. We study complexity and approximation of min weighted node coloring in planar, bipartite and split graphs. We show that this problem is NP-complete in planar graphs, even if they are trianglefree and their maximum degree is bounded above by 4. Then, we prove that min weighted node coloring is NP-complete in P8-free bipartite graphs, but polynomial for P5-free bipartite graphs. We next focus ourselves on approximability in general bipartite graphs and improve earlier approximation results by giving approximation ratios matching inapproximability bounds. We next deal with min weighted edge coloring in bipartite graphs. We show that this problem remains strongly NP-complete, even in the case where the input-graph is both cubic and planar. Furthermore, we provide an inapproximability bound of 7/6 − ε, for any ε > 0 and we give an approximation algorithm with the same ratio. Finally, we show that min weighted node coloring in split graphs can be solved by a polynomial time approximation scheme.

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Section: Introductionmentioning

confidence: 73%

“…The NP-completeness of min weighted node coloring has been established in [4] for general bipartite graphs. We show here that this remains true even if we restrict to planar bipartite graphs or to P 21 -free bipartite graphs (for definitions graph-theoretical notions used in this paper, the interested reader is referred to Berge [1]).…”

Section: Introductionmentioning

confidence: 99%

Weighted Coloring on Planar, Bipartite and Split Graphs: Complexity and Improved Approximation

Werra

Demange

Escoffier

et al. 2004

Algorithms and Computation

Self Cite

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show abstract

“…For a compendium of graph classes and the corresponding computational complexity of the coloring problem on them, see [6]. Max-coloring is substantially harder than the graph coloring problem, in particular it is NP-hard in the strong sense in split graphs [5], and so in particular in perfect graphs and in P 5 -free graphs. Restricted to bipartite graphs, it is NP-hard in P 8 -free bipartite graphs but polynomial-time solvable in P 5 -free bipartite graphs [4].…”

Section: Introductionmentioning

confidence: 99%

A note on the Cornaz–Jost transformation to solve the graph coloring problem

Bonomo

Giandomenico

Rossi

2013

Information Processing Letters

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“…The coloring case with f (S) = max{w i |i ∈ S} has been studied in [5], where it is proved that this problem is NP-hard even in bipartite and other restricted families of graphs. Other types of weighted coloring and partitioning problems are studied for instance in [1,3,4,12,13].…”

Section: Introductionmentioning

confidence: 99%

“…A notable example of such a problem is BIN PACK-ING, however, it is shown in [6], that this problem has an approximation scheme with respect to the saving criterion. Some approximation results are given in [5] for the coloring version of the problem with f (S) = max{w i |i ∈ S}, and in particular a 1 2 -approximation in general graphs. We will generalize and strengthen this result by obtaining the same bound for general independence systems and a variety of optimization criteria, and by improving the bound when there are only two different weights in the input.…”

Section: Introductionmentioning

confidence: 99%