75 citations · 671 across the 41 of their papers we have counts for
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An Electronic Compendium of Extreme Functions for the Gomory--Johnson Infinite Group Problem
Matthias Köppe, Yuan Zhou
In this note we announce the availability of an electronic compendium of extreme functions for Gomory--Johnson's infinite group problem. These functions serve as the strongest cut-…
Three Ehrhart Quasi-polynomials
Velleda Baldoni, Nicole Berline, Jesús A. De Loera +2
Let be a semi-rational parametric polytope, where is a real multi-parameter. We study intermediate sums of polynomial functions on ,…
Light on the Infinite Group Relaxation
Amitabh Basu, Robert Hildebrand, Matthias Köppe
This is a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their gro…
Intermediate Sums on Polyhedra II: Bidegree and Poisson Formula
Velleda Baldoni, Nicole Berline, Jesús A. De Loera +2
We continue our study of intermediate sums over polyhedra, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-poly…
Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. III. Foundations for the k-Dimensional Case with Applications to k=2
Amitabh Basu, Robert Hildebrand, Matthias Köppe
We develop foundational tools for classifying the extreme valid functions for the k-dimensional infinite group problem. In particular, (1) we present the general regular solution t…