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The Integer Hull of a Rational Polyhedron
Rekha Thomas
Date: Thursday, October 11, 2007 The integer hull of a rational polyhedron is the convex hull of all the integer points in it. This is again a polyhedron and is the central geometric object in discrete optimization. While the complexity of the outer polyhedron is essentially combinatorial, the integer hull is controlled by arithmetic and number theoretic information which makes it far more complicated. In this talk I will survey the methods in optimization that are used to understand integer hulls and describe recent work in this area by Tristram Bogart and myself where we introduce a new notion of complexity for integer hulls called the small Chvatal rank of a polyhedron. |