Reoptimization of maximum weight induced hereditary subgraph problems

Nicolas Boria (1) , Jérôme Monnot (1) , Vangelis Paschos (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

The reoptimization issue studied in this paper can be described as follows: given an instance I of some problem Π, an optimal solution OPT for Π in I and an instance I′ resulting from a local perturbation of I that consists of insertions or removals of a small number of data, we wish to use OPT in order to solve Π in I′, either optimally or by guaranteeing an approximation ratio better than that guaranteed by an ex nihilo computation and with running time better that that needed for such a computation. We use this setting in order to study weighted versions of several representatives of a broad class of problems known in the literature as maximum induced hereditary subgraph problems. The main problems studied are MAX INDEPENDENT SET, max k-COLORABLE SUBGRAPH, MAX Pk-FREE SUBGRAPH, MAX SPLIT SUBGRAPH and MAX PLANAR SUBGRAPH. We also show, how the techniques presented allow us to handle also bin packing.

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

Nicolas Boria, Jérôme Monnot, Vangelis Paschos. Reoptimization of maximum weight induced hereditary subgraph problems. 2011. ⟨hal-00875543⟩