Reductions for the Stable Set Problem

One approach to finding a maximum stable set (MSS) in a graph isto try to reduce the size of the problem by transforming the problem into an equivalent problem on a sma ller graph. This paper introduces several new reductions for the MSS problem, extends several well-known reductionsto the maximum weight stable set (MWSS) problem, demonstrates how reductions for the generalized stable setproblem can be used in conjunction with probing to produce powerful new reductions for both the MSS and MWSS problems, a nd shows how hypergraphs can be used to expand the capabilities of clique projections. The effectivenessof these new reduction techniques are illustrated on the DIM ACS benchmark graphs, planar graphs, and a set of challenging MS S problems arising from Steiner Triple Systems.

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