Computing the integer programming gap

Authors:
Serkan Hoşten;Bernd Sturmfels
Affiliations:
San Francisco State University, Department of Mathematics, 1600 Holloway Avenue, 94530, San Francisco, CA, USA;University of California, Department of Mathematics, 1600 Holloway Avenue, 94720, Berkeley, CA, USA
Venue:
Combinatorica
Year:
2007

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Abstract

We determine the maximal gap between the optimal values of an integer program and its linear programming relaxation, where the matrix and cost function are fixed but the right hand side is unspecified. Our formula involves irreducible decomposition of monomial ideals. The gap can be computed in polynomial time when the dimension is fixed.