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The Graver Complexity of Integer Programming
Yael Berstein and Shmuel Onn
Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Technion, Haifa 32000, Israel
yaelber@tx.technion.ac.il, onn@ie.technion.ac.il
Annals of Combinatorics 13 (3) pp.289-296 September, 2009
AMS Subject Classification: 05A, 15A, 51M, 52A
Abstract:
In this article we establish an exponential lower bound on the Graver complexity of integer programs. This provides new type of evidence supporting the presumable intractability of integer programming. Specifically, we show that the Graver complexity of the incidence matrix of the complete bipartite graph K{3,m} satisfies g(m)=\Omega(2m), with g(m)> 17• 2{m-3}-7 for every m>3.
Keywords: Graver basis, Grobner basis, Graver complexity, Markov complexity, contingency table, transportation polytope, transportation problem, integer programming, computational complexity

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