Carathéodory bounds for integer cones

Authors:
Friedrich Eisenbrand;Gennady Shmonin
Affiliations:
Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany;Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany
Venue:
Operations Research Letters
Year:
2006

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Abstract

We provide analogues of Caratheodory's theorem for integer cones and apply our bounds to integer programming and to the cutting stock problem. In particular, we provide an NP certificate for the latter, whose existence has not been known so far.