64 citations · 418 across the 52 of their papers we have counts for
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The Hierarchy of Circuit Diameters and Transportation Polytopes
Steffen Borgwardt, Jesús A. De Loera, Elisabeth Finhold +1
The study of the diameter of the graph of polyhedra is a classical problem in the theory of linear programming. While transportation polytopes are at the core of operations researc…
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 ,…
Edges vs Circuits: a Hierarchy of Diameters in Polyhedra
Steffen Borgwardt, Jesús A. De Loera, Elisabeth Finhold
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation i…
Parametric Polyhedra with at least Lattice Points: Their Semigroup Structure and the k-Frobenius Problem
Iskander Aliev, Jesus A. De Loera, Quentin Louveaux
Given an integral matrix , the well-studied affine semigroup $\mbox{ Sg} (A)=\{ b : Ax=b, \ x \in {\mathbb Z}^n, x \geq 0\}$ can be stratified by the number of latt…
On Augmentation Algorithms for Linear and Integer-Linear Programming: From Edmonds-Karp to Bland and Beyond
Jesus A. De Loera, Raymond Hemmecke, Jon Lee
Motivated by Bland's linear-programming generalization of the renowned Edmonds-Karp efficient refinement of the Ford-Fulkerson maximum-flow algorithm, we discuss three closely-rela…
A Quantitative Doignon-Bell-Scarf Theorem
Iskander Aliev, Robert Bassett, Jesus A. De Loera +1
The famous Doignon-Bell-Scarf Theorem is a Helly-type result about the existence of integer solutions on systems of linear inequalities. The purpose of this paper is to present the…
A Rainbow Ramsey Analogue of Rado's Theorem
Jesús A. De Loera, Reuben N. La Haye, Amanda Montejano +2
We present a Rainbow Ramsey version of the well-known Ramsey-type theorem of Richard Rado. We use techniques from the Geometry of Numbers. We also disprove two conjectures proposed…
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…