On integer points in polyhedra: A lower bound
نویسندگان
چکیده
منابع مشابه
On integer points in polyhedra
We give an upper bound on the number of vertices of PI, the integer hull of a polyhedron P, in terms of the dimension n of the space, the number m of inequalities required to describe P, and the size ~ of these inequalities. For fixed n the bound is O(mn~n-1). We also describe an algorithm which determines the number of integer points in a polyhedron to within a multiplicative factor of 1 qE in...
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We investigate the problem of sampling integer points in rational polyhedra provided an oracle for counting these integer points. When dimension is bounded, this assumption is justified in view of a recent algorithm due to Barvinok [B1,B2,BP]. We show that the exactly uniform sampling is possible in full generality, when the oracle is called polynomial number of times. Further, when Barvinok’s ...
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We consider the Minkowski sum of subsets of integer lattice, each of which is a set of integer points of a face of an extended submodular [Kashiwabara–Takabatake, Discrete Appl. Math. 131 (2003) 433] integer polyhedron supported by a common positive vector. We show a sufficient condition for the sum to contain all the integer points of its convex hull and a sufficient condition for the sum to i...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 1992
ISSN: 0209-9683,1439-6912
DOI: 10.1007/bf01204716