A branch-and-price approach for the maximum weight independent set problem

The maximum weight-independent set problem (MWISP) is one of the most well-known and well-studied problems in combinatorial optimization. This article presents a novel approach to solve MWISP exactly by decomposing the original graph into vertex-induced subgraphs. The approach solves MWISP for the original graph by solving MWISP on the subgraphs to generate columns for a branch-and-price framework. The authors investigate different implementation techniques that can be associated with the approach, and offer computational results to identify the strengths and weaknesses of each implementation technique.