REOPTIMIZATION UNDER VERTEX INSERTION: MAX Pk-FREE SUBGRAPH AND MAX PLANAR SUBGRAPH

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 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 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 to study weighted versions of MAX Pk-FREE SUBGRAPH and MAX PLANAR SUBGRAPH, which are representatives of a broad class of problems known in the literature as maximum induced hereditary subgraph problems. We also show that the techniques presented allow us to handle BIN PACKING.