Cost-based labeling of groups of mass spectra
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
An Alternative Algorithm for Counting Lattice Points in a Convex Polytope
Mathematics of Operations Research
Simple Explicit Formula for Counting Lattice Points of Polyhedra
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Discrete Optimization
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Given a convex rational polytope ?( b) := { x ? R n+ |Ax = b}, we consider the functionb ?f( b), which counts the nonnegative integral points of ?( b). A closed form expression of its Z-transformz?F( z) is easily obtained so thatf( b) can be computed as the inverse Z-transform of F. We then provide two variants of an inversion algorithm. As a by-product, one of the algorithms provides the Ehrhart polynomial of a convex integer polytope ?. We also provide an alternative that avoids the complex integration of F( z) and whose main computational effort is to solve a linear system. This latter approach is particularly attractive for relatively small values ofm, wherem is the number of nontrivial constraints (or rows ofA).