Nondecomposable solutions to group equations and an application to polyhedral combinatorics

This paper is based on the study of the set of nondecomposable integer solutions in a Gomory corner polyhedron, which was recently used in a reformulation method for integer linear programs. In this paper, we present an algorithm for efficiently computing this set. We precompute a database of nondecomposable solutions for cyclic groups up to order 52. As a second application of this database, we introduce an algorithm for computing nontrivial simultaneous lifting coefficients. The lifting coefficients are exact for a discrete relaxation of the integer program that consists of a group relaxation plus bound constraints.

• Type: Journal
• Year: 2006
• Where: 4OR
• Authors: Matthias Jach, Matthias Köppe, Robert Weismantel
• Keywords: 4OR 2006, Integer, Lifting Coefficients, Nondecomposable Integer Solutions