Abstract
Let K be a polyhedron in \({\mathbb R}^d\), given by a system of m linear inequalities, with rational number coefficients bounded over in absolute value by L. In this series of two papers, we propose an algorithm for computing an irredundant representation of the integer points of K, in terms of “simpler” polyhedra, each of them having at least one integer point. Using the terminology of W. Pugh: for any such polyhedron P, no integer point of its grey shadow extends to an integer point of P. We show that, under mild assumptions, our algorithm runs in exponential time w.r.t. d and in polynomial w.r.t m and L. We report on a software experimentation. In this series of two papers, the first one presents our algorithm and the second one discusses our complexity estimates.
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Acknowledgements
The authors would like to thank IBM Canada Ltd (CAS project 880) and NSERC of Canada (CRD grant CRDPJ500717-16), as well as the University of Chinese Academy of Sciences, UCAS Joint PhD Training Program, for supporting their work.
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Jing, RJ., Moreno Maza, M. (2017). Computing the Integer Points of a Polyhedron, I: Algorithm. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2017. Lecture Notes in Computer Science(), vol 10490. Springer, Cham. https://doi.org/10.1007/978-3-319-66320-3_17
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