34 citations · 60 across the 20 of their papers we have counts for
6 papers · 1 filter
Forall-exist statements in pseudopolynomial time
Eleonore Bach, Friedrich Eisenbrand, Thomas Rothvoss +1
Given a convex set and an integer matrix , we consider statements of the form s.t. $Wx \leq…
From approximate to exact integer programming
Daniel Dadush, Friedrich Eisenbrand, Thomas Rothvoss
Approximate integer programming is the following: For a convex body , either determine whether is empty, or find an integer point in…
An Algorithmic Theory of Integer Programming
Friedrich Eisenbrand, Christoph Hunkenschröder, Kim-Manuel Klein +3
We study the general integer programming problem where the number of variables is a variable part of the input. We consider two natural parameters of the constraint matrix :…
The Support of Integer Optimal Solutions
Iskander Aliev, Jesus De Loera, Fritz Eisenbrand +2
The support of a vector is the number of nonzero-components. We show that given an integral matrix , the integer linear optimization problem $\max\left\{\boldsymbol{…
A Note on Non-Degenerate Integer Programs with Small Sub-Determinants
Stephan Artmann, Friedrich Eisenbrand, Christoph Glanzer +3
The intention of this note is two-fold. First, we study integer optimization problems in standard form defined by and present an algorithm to solve s…
Parametric Integer Programming in Fixed Dimension
Friedrich Eisenbrand, Gennady Shmonin
We consider the following problem: Given a rational matrix $A \in \setQ^{m \times n}$ and a rational polyhedron $Q \subseteq\setR^{m+p}$, decide if for all vectors $b \in \setR^m$,…