An integer analogue of Carathe´odory's theorem
Journal of Combinatorial Theory Series B
Theory of linear and integer programming
Theory of linear and integer programming
Total dual integrality implies local strong unimodularity
Mathematical Programming: Series A and B
Variation of cost functions in integer programming
Mathematical Programming: Series A and B
Buchberger Algorithm and Integer Programming
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Hilbert Bases, Caratheodory's Theorem and Combinatorial Optimization
Proceedings of the 1st Integer Programming and Combinatorial Optimization Conference
Combinatorica
Grbner Deformations of Hypergeometric Differential Equations
Grbner Deformations of Hypergeometric Differential Equations
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In this paper we provide new characterizing properties of TDI systems. A corollary is Sturmfels' theorem relating toric initial ideals generated by square-free monomials to unimodular triangulations. A reformulation of these test-sets to polynomial ideals actually generalizes the existence of square-free monomials to arbitrary TDI systems, providing new relations between integer programming and Gröbner bases of toric ideals. We finally show that stable set polytopes of perfect graphs are characterized by a refined fan that is a triangulation consisting only of unimodular cones, a fact that endows the Weak Perfect Graph Theorem with a computationally advantageous geometric feature. Three ways of implementing the results are described and some experience about one of these is reported.