Abstract.
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.
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Received: November 2004 / Revised version: June 2005
AMS classification:
90C10, 90C57
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Jach, M., Köppe, M. & Weismantel, R. Nondecomposable solutions to group equations and an application to polyhedral combinatorics. 4OR 4, 29–46 (2006). https://doi.org/10.1007/s10288-005-0073-y
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DOI: https://doi.org/10.1007/s10288-005-0073-y