Barvinok, Alexander I. A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed. (English) Zbl 0821.90085 Math. Oper. Res. 19, No. 4, 769-779 (1994). Summary: 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. Cited in 7 ReviewsCited in 90 Documents MSC: 90C10 Integer programming 90C60 Abstract computational complexity for mathematical programming problems 52B12 Special polytopes (linear programming, centrally symmetric, etc.) 52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) 52B55 Computational aspects related to convexity Keywords:polynomial time algorithm; counting integral points in polyhedra PDF BibTeX XML Cite \textit{A. I. Barvinok}, Math. Oper. Res. 19, No. 4, 769--779 (1994; Zbl 0821.90085) Full Text: DOI OpenURL