Symmetries in Linear and Integer Programs

Details Symmetries in Linear and Integer Programs Symmetries in Linear and Integer Programs

2009-08-23

arxiv.org/abs/0908.3329v1

Mathematics

Combinatorics

23 pages, 2 figures

Scientific paper

The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution in the fixed point set of its symmetry group. Using this result, we develop an algorithm that allows for reducing the dimension of any linear program having a non-trivial group of symmetries.

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