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# Counting Integer Points in Parametric Polytopes Using Barvinok's Rational Functions

@article{Verdoolaege2006CountingIP, title={Counting Integer Points in Parametric Polytopes Using Barvinok's Rational Functions}, author={Sven Verdoolaege and Rachid Seghir and Kristof Beyls and Vincent Loechner and Maurice Bruynooghe}, journal={Algorithmica}, year={2006}, volume={48}, pages={37-66} }

- Published 2006 in Algorithmica
DOI:10.1007/s00453-006-1231-0

Many compiler optimization techniques depend on the ability to calculate the number of elements that satisfy certain conditions. If these conditions can be represented by linear constraints, then such problems are equivalent to counting the number of integer points in (possibly) parametric polytopes. It is well known that the enumerator of such a set can be represented by an explicit function consisting of a set of quasi-polynomials, each associated with a chamber in the parameter space… CONTINUE READING

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