An efficient algorithm for generalized minimum spanning tree problem

The Generalized Minimum Spanning Tree problem (GMST) has attracted much attention during the last few years. Since it is in-tractable, many heuristic algorithms have been proposed to solve large GMST instances. Motivated by the effectiveness and effi-ciency of the muscle (the union of all optimal solutions) for solv-ing other NP-hard problems, we investigate how to incorporate the muscle into heuristic design for GMST. Firstly, we demon-strate that it's NP-hard to obtain the muscle for GMST. Then we show that the muscle can be well approximated by the principle and subordinate candidate sets, which can be calculated on a re-duced version of GMST. Therefore, a Dynamic cAndidate set based Search Algorithm (DASA) is presented in this paper for GMST. In contrast to existing heuristics, DASA employs those candidate sets to initialize and optimize solutions. During the search process, those candidate sets are dynamically adjusted to include in new features provided by good solutions. Since those candidate sets cover almost all optimal solutions, the search space of DASA can be dramatically reduced so that elite solutions can be easily found in a short time. Extensive experiments demon-strate that our new algorithm slightly outperforms existing heuris-tic algorithms in terms of solution quality.