Novel Deterministic Heuristics for Building Minimum Spanning Trees with Constrained Diameter

  • C. Patvardhan
  • V. Prem Prakash
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5909)


Given a connected, weighted, undirected graph G with n vertices and a positive integer bound D, the problem of computing the lowest cost spanning tree from amongst all spanning trees of the graph containing paths with at most D edges is known to be NP-Hard for 4 ≤ D < n-1. This is termed as the Diameter Constrained, or Bounded Diameter Minimum Spanning Tree Problem (BDMST). A well known greedy heuristic for this problem is based on Prim’s algorithm, and computes BDMSTs in O(n4) time. A modified version of this heuristic using a tree-center based approach runs an order faster. A greedy randomized heuristic for the problem runs in O(n3) time and produces better (lower cost) spanning trees on Euclidean benchmark problem instances when the diameter bound is small. This paper presents two novel heuristics that compute low cost diameter-constrained spanning trees in O(n3) and O(n2) time respectively. The performance of these heuristics vis-à-vis the extant heuristics is shown to be better on a wide range of Euclidean benchmark instances used in the literature for the BDMST Problem.


Heuristics Diameter Constrained Minimum Spanning Tree Bounded Diameter Greedy 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • C. Patvardhan
    • 1
  • V. Prem Prakash
    • 2
  1. 1.Faculty of EngineeringDayalbagh Educational InstituteAgraIndia
  2. 2.Department of Information TechnologyAnand Engineering CollegeAgraIndia

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