A Kruskal-Based Heuristic for the Rooted Delay-Constrained Minimum Spanning Tree Problem

The rooted delay-constrained minimum spanning tree problem is an NP-hard combinatorial optimization problem arising for example in the design of centralized broadcasting networks where quality of service constraints are of concern. We present a construction heuristic based on Kruskal’s algorithm for finding a minimum cost spanning tree which eliminates some drawbacks of existing heuristic methods. To improve the solution we introduce a greedy randomized adaptive search procedure (GRASP) and a variable neighborhood descent (VND) using two different neighborhood structures. Experimental results indicate that our approach produces solutions of better quality in shorter runtime when having strict delay-bounds compared to an existing centralized construction method based on Prim’s algorithm. Especially when testing on Euclidian instances our Kruskal-based heuristic outperforms the Prim-based approach in all scenarios. Moreover our construction heuristic seems to be a better starting point for subsequent improvement methods.