A primal Barvinok algorithm based on irrational decompositions

Details A primal Barvinok algorithm based on irrational decompositions A primal Barvinok algorithm based on irrational decompositions

2006-03-13

arxiv.org/abs/math/0603308v4

Mathematics

Combinatorics

v3: New all-primal algorithm. v4: Extended introduction, updated computational results. To appear in SIAM Journal on Discrete

Scientific paper

We introduce variants of Barvinok's algorithm 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.

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