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Approximation of the Degree-Constrained Minimum Spanning Hierarchies

  • Miklós Molnár
  • Sylvain Durand
  • Massinissa Merabet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8576)

Abstract

Degree-constrained spanning problems are well known and are mainly used to solve capacity constrained routing problems. The degree-constrained spanning tree problems are NP-hard and computing the minimum cost spanning tree is not approximable. Often, applications (such as some degree-constrained communications) do not need trees as solutions. Recently, a more flexible, connected, graph related structure called hierarchy was proposed to span a set of vertices under constraints. This structure permits a new formulation of some degree-constrained spanning problems. In this paper we show that although the newly formulated problem is still NP-hard, it is approximable with a constant ratio. In the worst case, this ratio is bounded by 3/2. We provide a simple heuristic and prove its approximation ratio is the best possible for any algorithm based on a minimum spanning tree.

Keywords

Graph theory Networks Degree-Constrained Spanning Problem Spanning Hierarchy Approximation 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Miklós Molnár
    • 1
  • Sylvain Durand
    • 1
  • Massinissa Merabet
    • 1
  1. 1.Laboratory LIRMM UMR 5506, CC477University Montpellier 2Montpellier Cedex 5France

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