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  for  Π 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 in order to solve Π 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, maxk-colorable subgraph  and max split subgraph  under vertex insertions and deletions.