Delegate and Conquer: An LP-Based Approximation Algorithm for Minimum Degree MSTs

  • R. Ravi
  • Mohit Singh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


In this paper, we study the minimum degree minimum spanning tree problem: Given a graph G = (V,E) and a non-negative cost function c on the edges, the objective is to find a minimum cost spanning tree T under the cost function c such that the maximum degree of any node in T is minimized.

We obtain an algorithm which returns an MST of maximum degree at most Δ*+k where Δ* is the minimum maximum degree of any MST and k is the distinct number of costs in any MST of G. We use a lower bound given by a linear programming relaxation to the problem and strengthen known graph-theoretic results on minimum degree subgraphs [3,5] to prove our result. Previous results for the problem [1,4] used a combinatorial lower bound which is weaker than the LP bound we use.


Span Tree Maximum Degree Minimum Span Tree Polynomial Time Algorithm Linear Programming Relaxation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • R. Ravi
    • 1
  • Mohit Singh
    • 1
  1. 1.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA

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