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A primal Barvinok algorithm based on irrational decompositions. (English) Zbl 1135.05003

Summary: We introduce variants of A.I. Barvinok’s algorithm [Math. Oper. Res. 19, No. 4, 769–779 (1994; Zbl 0821.90085)] for counting lattice points in polyhedra. The new algorithms are based on irrational signed decomposition in the primal space and the construction of rational generating functions for cones with low index. We give computational results that show that the new algorithms are faster than the existing algorithms by a large factor.

MSC:

05A15 Exact enumeration problems, generating functions
52B12 Special polytopes (linear programming, centrally symmetric, etc.)
52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry)
68W30 Symbolic computation and algebraic computation

Citations:

Zbl 0821.90085

Software:

LattE; NTL
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