A cutting-plane approach to the edge-weighted maximal clique problem
The following maximal clique problem is considered. Given a complete undirected graph \(G\) with real edge-weights, find a clique \(C\) in \(G\) such that the sum of edge-weights in \(C\) is maximal. It is shown that contrary to the fact that cutting planes algorithms have been successfully applied to related problems like the edge-weighted partition problem or the linear ordering problem similar methods applied to the maximal clique problem fails. A computational study shows that even for graphs with 15 or 25 vertices the results are very poor.
scientific article; zbMATH DE number 474806
scientific article