Reoptimization of some maximum weight induced hereditary subgraph problems

Authors:
Nicolas Boria;Jérôme Monnot;Vangelis Th. Paschos
Affiliations:
LAMSADE, CNRS UMR 7243 and Université Paris-Dauphine, France;LAMSADE, CNRS UMR 7243 and Université Paris-Dauphine, France;LAMSADE, CNRS UMR 7243 and Université Paris-Dauphine, France and Institut Universitaire de France, France
Venue:
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Year:
2012

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Abstract

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 than 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, maxk-colorable subgraph and max split subgraph under vertex insertions and deletions.