Mathematical Methods of Operations Research

, Volume 76, Issue 1, pp 95–123 | Cite as

Steiner tree packing revisited

Original Article

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.

Keywords

Steiner tree packing Integer programming Grid graph 

Mathematics Subject Classification

90C90 90C11 90C35 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Faculty of Mathematics, Mechanics, and InformaticsVietnam National UniversityHanoiVietnam
  2. 2.Zuse Institute BerlinBerlinGermany

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