64 citations · 418 across the 52 of their papers we have counts for
4 papers · 1 filter
Quantitative combinatorial geometry for continuous parameters
J. A. De Loera, R. N. La Haye, D. Rolnick +1
We prove variations of Carathéodory's, Helly's and Tverberg's theorems where the sets involved are measured according to continuous functions such as the volume or diameter. Among…
The Diameters of Network-flow Polytopes satisfy the Hirsch Conjecture
S. Borgwardt, J. A. De Loera, E. Finhold
We solve a problem in the combinatorics of polyhedra motivated by the network simplex method. We show that the Hirsch conjecture holds for the diameter of the graphs of all network…
Sparse solutions of linear Diophantine equations
Iskander Aliev, Jesus A. De Loera, Timm Oertel +1
We present structural results on solutions to the Diophantine system , with the smallest number of non…
Approximating the maximum of a polynomial over a polytope: Handelman decomposition and continuous generating functions
Jesús De Loera, Brandon Dutra, Matthias Köppe
We investigate a way to approximate the maximum of a polynomial over a polytopal region by using Handelman's polynomial decomposition and continuous multivariate generating functio…