Abstract
We address the generalized minimum spanning tree problem (GMST) which requires spanning at least one vertex out of every set of disjoint vertices in a graph. We show that the geometric version of this problem is NP -hard, and we propose two stochastic heuristics. The first one is a very fast randomized greedy search algorithm and the second one being a genetic algorithm. Also, we investigate some existing integer programming formulations and present an new one. A new Lagrangian based lower bound is proposed and implemented to assess the performance of the heuristics. Computational experiments performed on a large set of randomly generated instances with up to 1000 vertices and 10,000 edges provide evidence of the good performance of the proposed heuristics.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
