A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed

Authors:
A. I. Barvinok
Affiliations:
Dept. of Math., R. Inst. of Technol., Stockholm, Sweden
Venue:
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Year:
1993

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Integer programming

Algorithms and theory of computation handbook

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Abstract

We prove that for any dimension d there exists a polynomial time algorithm for counting integral points in polyhedra in the d-dimensional Euclidean space. Previously such algorithms were known for dimensions d=1,2,3, and 4 only.