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

  • Mario Ruthmair
  • Günther R. Raidl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5717)


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.


Span Tree Root Node Greedy Randomize Adaptive Search Procedure Minimum Span Tree Problem Construction Heuristic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mario Ruthmair
    • 1
  • Günther R. Raidl
    • 1
  1. 1.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

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