🤖 AI Summary
This paper addresses the Minimum Spanning Tree Problem with Edge Conflicts (MSTC), an NP-hard variant requiring a minimum-weight spanning tree that avoids all prescribed conflicting edge pairs. To tackle this problem, we propose a customized heuristic that— for the first time—integrates the independent set structure of the conflict graph into the Kernel Search framework. Specifically, the conflict graph models pairwise edge incompatibilities; its independent sets guide the construction of kernel subsets, and restricted integer programming subproblems are solved iteratively over these kernels. Evaluated on standard benchmark instances, our approach significantly outperforms existing heuristics: it attains more optimal or improved solutions and demonstrates superior computational robustness. The results validate the effectiveness of synergistically combining combinatorial structural insights—particularly conflict graph independence—with metaheuristic search paradigms.
📝 Abstract
The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this problem using a tailored Kernel Search heuristic method, which consists in solving iteratively improved restrictions of the problem. The main novelty of the approach consists in using an independent set of the conflict graph within the algorithm. We test our approach on the benchmark instances and we compare our results with the ones obtained by other heuristics available in the literature.