Un nuevo algoritmo de ramificación y acotamiento para el problema de la bisección de vértices

Abstract

In this paper we approach the exact solution of the vertex bisection problem. It is a NP-hard problem which ocurrs in the context of 331 communication networks. Currently, the best state-of-the-arte algorithm is the BBVBMP, it use the branch-and-bound methodology. In this paper, we propose a new algorithm based in the same methodology. Our proposal takes advantage of a constructive heuristic to initiliaize the upper bound. This heuristic considers the degree of the vertex candidates. Also, the proposed algorithm explores the search tree in the combinatorial space with a maximum height of n/2 nodes, decreasing the size of the tree. The performance of the new heuristics was measure with a benchmark set with known optimals by construction. The experimental results shows that the heuristic in the porposed algorithm outperforms in eficiency the heuristic incorporated in BBVBMP. Finally, the performace of the proposed algorithm is compared against the BBVBMP when solving the vertex bisection problem benchmark. The results show that the proposed algorithm reach the same quality solution as BBVBMP, with a reduction in the execution time of 15 %.