Let K be a polyhedron in Rd, 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.
CITATION STYLE
Jing, R. J., & Moreno Maza, M. (2017). Computing the Integer Points of a Polyhedron, I: Algorithm. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10490 LNCS, pp. 225–241). Springer Verlag. https://doi.org/10.1007/978-3-319-66320-3_17
Mendeley helps you to discover research relevant for your work.