In this paper, we introduce two powerful graph reductions for the maximum weighted stable set (mwss) in general graphs. We show that these reductions allow to reduce the mwss in claw-free graphs to the mwss in a class of quasi-line graphs, that we call bipolar-free. For this latter class, we provide a new algorithmic decomposition theorem running in polynomial time. We then exploit this decomposition result and our reduction tools again to transform the problem to either a single matching problem or a longest path computation in an acyclic auxiliary graph (in this latter part we use some results of Pulleyblank and Shepherd [10]). Putting all the pieces together, the main contribution of this paper is a new polynomial time algorithm for the mwss in claw-free graphs. A rough analysis of the complexity of this algorithm gives a time bound of O(n 6), where n is the number of vertices in the graph, and which we hope can be improved by a finer analysis. Incidentally, we prove that the mwss problem can be solved efficiently for any class of graphs that admits a "suitable" decomposition into pieces where the mwss is easy. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Oriolo, G., Pietropaoli, U., & Stauffer, G. (2008). A new algorithm for the maximum weighted stable set problem in claw-free graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5035 LNCS, pp. 77–96). https://doi.org/10.1007/978-3-540-68891-4_6
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