75 citations · 671 across the 41 of their papers we have counts for
5 papers · 1 filter
Ehrhart polynomials of matroid polytopes and polymatroids
Jesús A. De Loera, David C. Haws, Matthias Köppe
We investigate properties of Ehrhart polynomials for matroid polytopes, independence matroid polytopes, and polymatroids. In the first half of the paper we prove that for fixed ran…
Pareto Optima of Multicriteria Integer Linear Programs
Jesús A. De Loera, Raymond Hemmecke, Matthias Köppe
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space…
FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension
Jesús A. De Loera, Raymond Hemmecke, Matthias Köppe +1
We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, w…
Computing parametric rational generating functions with a primal Barvinok algorithm
Matthias Köppe, Sven Verdoolaege
Computations with Barvinok's short rational generating functions are traditionally being performed in the dual space, to avoid the combinatorial complexity of inclusion--exclusion…
Computation of Atomic Fibers of Z-Linear Maps
Elke Eisenschmidt, Raymond Hemmecke, Matthias Köppe
For given matrix , the set describes the preimage or fiber of under the -linear map , $x\mapsto…