75 citations · 671 across the 41 of their papers we have counts for
4 papers · 1 filter
The Triangle Closure is a Polyhedron
Amitabh Basu, Robert Hildebrand, Matthias Köppe
Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research ar…
A (k+1)-Slope Theorem for the k-Dimensional Infinite Group Relaxation
Amitabh Basu, Robert Hildebrand, Matthias Köppe +1
We prove that any minimal valid function for the k-dimensional infinite group relaxation that is piecewise linear with at most k+1 slopes and does not factor through a linear map w…
Software for Exact Integration of Polynomials over Polyhedra
Jesus De Loera, Brandon Dutra, Matthias Koeppe +3
We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms prese…
Unique Minimal Liftings for Simplicial Polytopes
Amitabh Basu, Gérard Cornuéjols, Matthias Köppe
For a minimal inequality derived from a maximal lattice-free simplicial polytope in , we investigate the region where minimal liftings are uniquely defined, and we characteri…