Abstract
In the clique partition problem (CPP), we need to find a spanning family of pairwise vertex-disjoint cliques of minimum total weight in a complete edge-weighted graph. In this paper, we consider the special case of the CPP, the so-called graph approximation problem (GAP), where the weights of edges are 1 or −1. It is one of the most computationally difficult cases of the CPP. We present our polyhedral approach to this problem based on the facet inequalities and the branch and cut framework. Computational experiments on the randomly generated instances indicate simple and hard classes of the GAP and maximal dimension for exact and an approximate solution with a given accuracy.
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