The max quasi-independent set problem

Nicolas Bourgeois (1) , Aristotelis Giannakos (1) , Giorgio Lucarelli (1, 2) , Ioannis Milis (3) , Vangelis Paschos (1) , Olivier Pottié (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 AUEB - Athens University of Economics and Business
3 CS-AUEB - Department of Informatics [Athens]

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-QIS, 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 $O^*{\frac{d-27/23}{d+1}u})$ on graphs of average degree bounded by d. For the most specifically defined -QIS and k-QIS problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.

Domaines: Algorithme et structure de données [cs.DS]; Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Nicolas Bourgeois, Aristotelis Giannakos, Giorgio Lucarelli, Ioannis Milis, Vangelis Paschos, et al.. The max quasi-independent set problem. 2010. ⟨hal-00880207⟩