On Barvinok's algorithm for counting lattice points in fixed dimension

Mathematics of Operations Research

Volumn 22, Issue 3, 1997, Pages 545-549

  Dyer, Martin ^a   Kannan, Ravi ^b  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b Carnegie Mellon University   (United States)

Author keywords

Counting problems; Fixed dimension; Lattice points; Polytopes

Indexed keywords

COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; POLYNOMIALS; PROBLEM SOLVING; VECTORS;

CONVEX POLYHEDRON; POLYNOMIAL TIME ALGORITHM;

ALGORITHMS;

EID: 0031210630     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.22.3.545     Document Type: Article

References (8)

1. Barvinok, A. I. (1994). A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed. Math. Oper. Res. 19 769-779.
2. Brion, M. (1992). Polyèdres et réseaux. L'enseignement Mathématique 38 71-78.
3. Dyer, M. E. (1991). On counting lattice points in polyhedra. SIAM J. Computing 20 695-707.
4. Khovanskii, A. G., A. V. Puhlikov (1992). A Riemann-Roch theorem for integrals and sums of quasipolynomials on virtual polytopes (Russian). Algebra i analiz, 4 188-216. Translated in St. Petersburg Math. J. 4 789-812.
5. Khovanskii, A. G., A. V. Puhlikov (1992). A Riemann-Roch theorem for integrals and sums of quasipolynomials on virtual polytopes (Russian). Algebra i analiz, 4 188-216. Translated in St. Petersburg Math. J. 4 789-812.
6. Schrijver, A. (1986). Theory of Linear and Integer Programming, John Wiley, Chichester.
7. Varchenko, A. N. (1987), Combinatorics and topology of the disposition of affine hyperplanes in real space (Russian). Funktsional. Anal, i Prilozhen. 21 N 1, 11-22. Translated in Funct. Anal. Appl. 21 9-19.
8. Varchenko, A. N. (1987), Combinatorics and topology of the disposition of affine hyperplanes in real space (Russian). Funktsional. Anal, i Prilozhen. 21 N 1, 11-22. Translated in Funct. Anal. Appl. 21 9-19.