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The max quasi-independent set problem

Bourgeois, Nicolas; Giannakos, Aristotelis; Lucarelli, Giorgio; Milis, Ioannis; Paschos, Vangelis; Pottié, Olivier (2012), The max quasi-independent set problem, Journal of Combinatorial Optimization, 23, 1, p. 94-117. 10.1007/s10878-010-9343-5

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Type
Article accepté pour publication ou publié
Date
2012
Journal name
Journal of Combinatorial Optimization
Volume
23
Number
1
Publisher
Springer
Pages
94-117
Publication identifier
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Author(s)
Bourgeois, Nicolas
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Giannakos, Aristotelis
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lucarelli, Giorgio cc

Milis, Ioannis

Paschos, Vangelis
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Pottié, Olivier
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
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(|Q|). For this problem, we show an exact solution method that runs within time O(2d+1d−2723n) on graphs of average degree bounded by d. For the most specifically defined γ-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.
Subjects / Keywords
Exact algorithms; Approximation algorithms; Quasi independent set