On Robust Algorithms for the Maximum Weight Stable Set Problem

Abstract

The Maximum Weight Stable Set (MWS) Problem is one of the fundamental algorithmic problems in graphs. It is NP-complete in general, and it has polynomial time solutions on many particular graph classes, some of them defined by forbidden subgraphs. A classical example is the result of Minty that the MWS problem is polynomially solvable for the class of claw-free graphs. The complexity of the MWS problem is unknown for the class of P5-free graphs. We give a survey on recently obtained efficient algorithms for the MWS problem for several graph classes defined by forbidden subgraphs where the algorithm avoids to recognize whether the (arbitrary) input graph is in the class i.e. the output is either a correct solution of the MWS problem or the fact that the input graph is not in the class. Such algorithms were called robust by Spinrad. The algorithms use the concepts of modular decomposition and of clique width of graphs.