Theory of linear and integer programming
Theory of linear and integer programming
A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
Mathematics of Operations Research
On Barvinok's algorithm for counting lattice points in fixed dimension
Mathematics of Operations Research
Hard Equality Constrained Integer Knapsacks
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Decomposition of Integer Programs and of Generating Sets
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Integer programming, Barvinok's counting algorithm and Gomory relaxations
Operations Research Letters
Mixed-integer nonlinear programming: some modeling and solution issues
IBM Journal of Research and Development - Business optimization
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This paper discusses five algorithms to solve linear integer programming problems that use the rational function techniques introduced by A. Barvinok. We report on the first ever experimental results based on these techniques.