The Complexity of Generic Primal Algorithms for Solving General Integer Programs
Mathematics of Operations Research
Non-standard approaches to integer programming
Discrete Applied Mathematics
An augment-and-branch-and-cut framework for mixed 0-1 programming
Combinatorial optimization - Eureka, you shrink!
Generalized Reduction to Compute Toric Ideals
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The combinatorics of modeling and analyzing biological systems
Natural Computing: an international journal
A saturation algorithm for homogeneous binomial ideals
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Representing and solving finite-domain constraint problems using systems of polynomials
Annals of Mathematics and Artificial Intelligence
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In this paper we modify Buchberger's S-pair reduction algorithm for computing a Gröbner basis of a toric ideal so as to apply it to an integer program (IP) in inequality form with fixed right-hand sides and fixed upper bounds on the variables. We formulate the algorithm in the original space and interpret the reduction steps geometrically. In fact, three variants of this algorithm are presented, and we give elementary proofs for their correctness. A relationship among these (exact) algorithms, iterative improvement heuristics, and the Kernighan--Lin procedure is established. Computational results are also presented.