Mathematical Programming

, Volume 137, Issue 1, pp 65–90

Algorithms for highly symmetric linear and integer programs

Full Length Paper Series A

DOI: 10.1007/s10107-011-0487-6

Cite this article as:
Bödi, R., Herr, K. & Joswig, M. Math. Program. (2013) 137: 65. doi:10.1007/s10107-011-0487-6

Abstract

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension. Combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension.

Keywords

Linear programming Integer programming Symmetry Permutation group 

Mathematics Subject Classification (2000)

90C10 (90C05, 52B12) 

Copyright information

© Springer and Mathematical Optimization Society 2011

Authors and Affiliations

  1. 1.School of EngineeringZürcher Hochschule für Angewandte WissenschaftenWinterthurSwitzerland
  2. 2.Fachbereich MathematikTU DarmstadtDarmstadtGermany

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