Efficient robust algorithms for the Maximum Weight Stable Set Problem in chair-free graph classes

Brandstädt, Andreas; Lê, Van Bang; Ridder, H. N. de

doi:10.1016/j.ipl.2003.11.002

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…To this end, they exploited the idea of modular decomposition, which also had led to efficient solutions to the maximum weight independent set problem in some other subclasses of fork-free graphs [10,11]. Modular decompositions will play a key role in our algorithm too.…”

Section: Other Classesmentioning

confidence: 99%

A polynomial algorithm to find an independent set of maximum weight in a fork-free graph

Lozin

Milanič

2008

Journal of Discrete Algorithms

102

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The class of fork-free graphs is an extension of claw-free graphs and their subclass of line graphs. The first polynomial-time solution to the maximum weight independent set problem in the class of line graphs, which is equivalent to the maximum matching problem in general graphs, has been proposed by Edmonds in 1965 and then extended to the entire class of claw-free graphs by Minty in 1980. Recently, Alekseev proposed a solution for the larger class of fork-free graphs, but only for the unweighted version of the problem, i.e., finding an independent set of maximum cardinality. In the present paper, we describe the first polynomial-time algorithm to solve the problem for weighted fork-free graphs.

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Section: Other Classesmentioning

confidence: 99%

A polynomial algorithm to find an independent set of maximum weight in a fork-free graph

Lozin

Milanič

2008

Journal of Discrete Algorithms

102

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“…It turns out that a suitable generalization of the EWIS problem can be solved in pseudo-polynomial time for graphs in a class G if it can be solved in pseudo-polynomial time for those induced subgraphs of graphs from G that are prime with respect to the modular decomposition. Together with the results from [1], this observation leads to pseudo-polynomial time algorithms for the EWIS problem in several graph classes that strictly generalize cographs, such as the (P 5 , fork )-free graphs or the (bull , fork )-free graphs.…”

Section: Cographs and Extensionsmentioning

confidence: 74%

The Exact Weighted Independent Set Problem in Perfect Graphs and Related Classes

Milanič

Monnot

2009

Electronic Notes in Discrete Mathematics

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“…Moreover, it is unbounded, even if we additionally forbid a co-gem. However, if a (P 5 ,chair)-free graph G contains a co-gem as an induced subgraph, then the clique-width of G is at most three [6]. Similarly, the clique-width of (chair,bull)-free graphs containing a co-gem is at most one [6].…”

Section: Various Classesmentioning

confidence: 99%

Recent developments on graphs of bounded clique-width

Kamiński

Lozin

Milanič

2009

Discrete Applied Mathematics

106

115

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a b s t r a c tWhether the clique-width of graphs in a certain class of graphs is bounded or not, is an important question from an algorithmic point of view, as many problems that are NPhard in general admit polynomial-time solutions when restricted to graphs of bounded clique-width. Over the last few years, many classes of graphs have been shown to have bounded clique-width. For many others, this parameter has been proved to be unbounded. This paper provides a survey of recent results addressing this problem.

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Efficient robust algorithms for the Maximum Weight Stable Set Problem in chair-free graph classes

Cited by 9 publications

References 21 publications

A polynomial algorithm to find an independent set of maximum weight in a fork-free graph

A polynomial algorithm to find an independent set of maximum weight in a fork-free graph

The Exact Weighted Independent Set Problem in Perfect Graphs and Related Classes

Recent developments on graphs of bounded clique-width

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