Lagrangean bounds for the optimum communication spanning tree problem

  1. Ivan Contreras 1
  2. Elena Fernández 1
  3. Alfredo Marín 2
  1. 1 Universitat Politècnica de Catalunya, España
  2. 2 Universidad de Murcia, España
Revista:
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ISSN: 1863-8279,  1134-5764

Any de publicació: 2010

Volum: 18

Número: 1

Pàgines: 140-157

Tipus: Article

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Resum

This paper considers the Optimum Communication Spanning Tree Problem. An integer programming formulation that yields tight LP bounds is proposed. Given that the computational effort required to obtain the LP bounds considerably increases with the size of the instances when using commercial solvers, we propose a Lagrangean relaxation that exploits the structure of the formulation. Since feasible solutions to the Lagrangean function are spanning trees, upper bounds are also obtained. These bounds are later improved with a simple local search. Computational experiments have been run on several benchmark instances from the literature. The results confirm the interest of the proposal since tight lower and upper bounds are obtained, for instances up to 100 nodes, in competitive computational times.

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Acknowledgements This research has been partially supported by the National Council of Science and Technology, México (grant 197243/217997), Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica (I+D+I) (projects MTM2006-14961-C05-(01,04)), Fundación Séneca (project 08716/PI/08) and ERDF funds. These supports are gratefully acknowledged. Also, the authors are grateful to one anonymous referee for his constructive comments that have contributed to improving the article.

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