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Article Dans Une Revue Journal of Combinatorial Optimization Année : 2012

The max quasi-independent set problem

Nicolas Bourgeois
Aristotelis Giannakos
  • Fonction : Auteur
  • PersonId : 947024
  • IdRef : 193460564
Giorgio Lucarelli
Ioannis Milis
  • Fonction : Auteur
Vangelis Th. Paschos
  • Fonction : Auteur
  • PersonId : 946990
  • IdRef : 069701873
Olivier Pottié
  • Fonction : Auteur

Résumé

In this paper, we deal with the problem of finding quasi-independent sets in graphs. This problem is formally defined in three versions, which are shown to be polynomially equivalent. The one that looks most general, namely, $f$-max quasi-independent set, consists of, given a graph and a non-decreasing function $f$, finding a maximum size subset $Q$ of the vertices of the graph, such that the number of edges in the induced subgraph is less than or equal to $f(\vert Q \vert)$. For this problem, we show an exact solution method that runs within time $O^\ast(2^{\frac{d-27/23}{d+1}n})$ on graphs of average degree bounded by $d$. For the most specifically defined $\gamma$-max quasi-independent set and $k$-max quasi-independent set problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.

Dates et versions

hal-01185274 , version 1 (19-08-2015)

Identifiants

Citer

Nicolas Bourgeois, Aristotelis Giannakos, Giorgio Lucarelli, Ioannis Milis, Vangelis Th. Paschos, et al.. The max quasi-independent set problem. Journal of Combinatorial Optimization, 2012, 23, pp.94-117. ⟨10.1007/s10878-010-9343-5⟩. ⟨hal-01185274⟩
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