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Algebraic Perturbation Barvinok
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| Organization: | Augusta University |
| Organization: | University of Michigan |
| Department: | Industrial and Operations Engineering Department |
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2015-12-07
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This algorithm generates a short rational generating function G(z) for a bounded input polyhedron P defined by a system of rational linear inequalities Ax <= b. This variation of Barvinok`s algorithm operates on an algebraic perturbation P(t) of the original polyhedron P, created so that P(t) is both full dimensional and has all simple vertices. As an option, the algorithm uses G(z) to count the integer points of P. For a complete description of the algorithm, see 1) Jon Lee, Daphne Skipper. An algebraic-perturbation variant of Barvinok's algorithm. LAGOS 2015, To appear in: Electronic Notes in Discrete Mathematics. 2) Jon Lee, Daphne Skipper. Computing with an algebraic-perturbation variant of Barvinok's algorithm. To appear in: Discrete Applied Mathematics.
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Barvinok’s algorithm, rational generating function, integer points, lattice point enumeration, polytope, polyhedron, linear integer optimization
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| AlgebraicPerturbationBarvinok.m (16.8 KB) - Mathematica Package |
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