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A Parallel Lagrangian Relaxation Algorithm for the Min-Degree Constrained Minimum Spanning Tree Problem

  • Leonardo Conegundes Martinez
  • Alexandre Salles da Cunha
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)

Abstract

Given an edge weighted undirected graph G and a positive integer d, the Min-Degree Constrained Minimum Spanning Tree Problem (MDMST) asks for a minimum cost spanning tree of G, such that each vertex is either a leaf or has degree at least d in the tree. The strongest known MDMST lower bounds, provided by a reformulation by intersection, are very expensive to be evaluated directly, by Linear Programming solvers. Therefore, we propose a Lagrangian Relaxation algorithm for approximating them. The reformulation makes use of a large number of variables and the relaxation involves the dualization of a large number of constraints. Attempting to speed up the computation of the Lagrangian Dual bounds, we implemented a parallel Subgradient Method. We also introduced a Lagrangian heuristic based on a Local Branching algorithm. With the proposed methods, respectively 26 and 14 new best upper and lower bounds are presented.

Keywords

Min-Degree Constrained Minimum Spanning Tree Problem Lagrangian Relaxation Local Branching Parallel Programming 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Leonardo Conegundes Martinez
    • 1
  • Alexandre Salles da Cunha
    • 1
  1. 1.Departamento de Ciência da ComputaçãoUniversidade Federal de Minas GeraisBelo HorizonteBrazil

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