Abstract
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.
The first author was supported by a Fulbright grant and by NSF grants DMS-9983797 and DMS-0401047. The research of the second author was supported by the “Marie Curie Training Network” ADONET of the European Community.
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O’Shea, E., Sebő, A. (2007). Characterizations of Total Dual Integrality. In: Fischetti, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2007. Lecture Notes in Computer Science, vol 4513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72792-7_29
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