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Steiner tree packing revisited

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  • Nam-Dũng Hoàng
  • Thorsten Koch

Abstract

The Steiner tree packing problem (STPP) in graphs is a long studied problem in combinatorial optimization. In contrast to many other problems, where there have been tremendous advances in practical problem solving, STPP remains very difficult. Most heuristics schemes are ineffective and even finding feasible solutions is already NP-hard. What makes this problem special is that in order to reach the overall optimal solution non-optimal solutions to the underlying NP-hard Steiner tree problems must be used. Any non-global approach to the STPP is likely to fail. Integer programming is currently the best approach for computing optimal solutions. In this paper we review some “classical” STPP instances which model the underlying real world application only in a reduced form. Through improved modelling, including some new cutting planes, and by employing recent advances in solver technology we are for the first time able to solve those instances in the original 3D grid graphs to optimimality. Copyright Springer-Verlag 2012

Suggested Citation

  • Nam-Dũng Hoàng & Thorsten Koch, 2012. "Steiner tree packing revisited," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(1), pages 95-123, August.
    • Handle: RePEc:spr:mathme:v:76:y:2012:i:1:p:95-123
    DOI: 10.1007/s00186-012-0391-8
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    References listed on IDEAS

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    1. Egon Balas & Clarence H. Martin, 1980. "Pivot and Complement--A Heuristic for 0-1 Programming," Management Science, INFORMS, vol. 26(1), pages 86-96, January.
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