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On integer points in polyhedra (1992)

Cook, W. ; Hartmann, M. ; Kannan, R. ; [et al.]

Springer

Combinatorica 12 (1992), S. 27-37

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ISSN: 1439-6912

Keywords: 52 A 25 ; 90 C 10

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We give an upper bound on the number of vertices ofP I , the integer hull of a polyhedronP, in terms of the dimensionn of the space, the numberm of inequalities required to describeP, and the size ϕ of these inequalities. For fixedn the bound isO(m n ϕ n− ). We also describe an algorithm which determines the number of integer points in a polyhedron to within a multiplicative factor of 1+ε in time polynomial inm, ϕ and 1/ε when the dimensionn is fixed.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01191202

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