Reoptimization of 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 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.