2009•arXiv (Cornell University)Open access

Symmetries in Integer Programs

Richard Bödi, Katrin Herr

Abstract

The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show that any integer program on n variables having an alternating group A_n as a group of symmetries can be solved in linear time in the number of variables.

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Key concepts: Integer (computer science), Integer points in convex polyhedra, Integer programming, Homogeneous space, Branch and price, Context (archaeology), Group (periodic table), Mathematics