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 Pi, an optimal solution OPT for Pi in I and an instance I' resulting from a local modification of I that consists of insertions or removals of a small number of data, we wish to use OPT in order to solve Pi in I'. The aim is to achieve either a better approximation ratio or a better running time (or both) than guaranteed by ex nihilo 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. (C) 2012 Elsevier B.V. All rights reserved.