Fundamental Domains for Integer Programs with Symmetries

We define a fundamental domain for a linear programming relaxation of a combinatorial integer program which is symmetric under a group action. We then describe a straightforward way to construct fundamental domains defined by the maximization of a linear function. The computation of this fundamental domain is at worst polynomial in the size of the group; however, for the symmetric group, which has exponential size, we show how to compute separation in polynomial time (in the size of the integer program). Fundamental domains are a simple and flexible approach to reducing the computation difficulties that often arise in integer programs with symmetries. Their construction is closely related to the constructions of orbitopes (by Kaibel and Pfetsch), but more general and easier to analyze, although the computations required may be somewhat more complex.

• Type: Conference
• Year: 2007
• Where: COCOA
• Authors: Eric J. Friedman
• Keywords: COCOA 2007, Combinatorial Integer Program, Fundamental Domains, Integer Programs