Reoptimization of Some Maximum Weight Induced Hereditary Subgraph Problems

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