Towards an Efficient Handling of the Maximum Triangle Packing Problem
Résumé
This work addresses the problem of finding the maximum number of unweighted vertex-disjoint triangles in an undirected graph G. It is a challenging NP-hard problem in combinatorics and it is well-known to be APX-hard. We propose two heuristics for this problem. The first is based on local substitutions, while the second uses a surrogate relaxation of the related integer linear program which is analog to a specific knapsack problem. A computational comparison of the two heuristics using randomly generated benchmarks has shown that the first heuristic outperforms the second heuristic regarding the obtained packing solutions and the respective computation times.