, Volume 12, Issue 1, pp 27–37

On integer points in polyhedra


  • W. Cook
    • Bell Communications Research, U.S.A. and Institut für Ökonometrie und Operations ResearchUniversität Bonn
  • M. Hartmann
    • Department of Operations ResearchUniversity of North Carolina
  • R. Kannan
    • Computer Science DepartmentCarnegie-Mellon University
  • C. McDiarmid
    • Institute of Economics and Statistics

DOI: 10.1007/BF01191202

Cite this article as:
Cook, W., Hartmann, M., Kannan, R. et al. Combinatorica (1992) 12: 27. doi:10.1007/BF01191202


We give an upper bound on the number of vertices ofPI, 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(mnϕn−). 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.

AMS subject classification code (1991)

52 A 2590 C 10

Copyright information

© Akadémiai Kiadó 1992