1 citations · 1 across the 8 of their papers we have counts for
9 papers
Polynomial Matrices in Integer Programming With Restricted Subdeterminants
Marcel Celaya, Stefan Kuhlmann, Robert Weismantel
We introduce a framework for tackling questions in discrete optimization associated with parametric constraint matrices. More precisely, the constraint matrices have entries that a…
A Threshold Number for the Shortest Vector Problem in the Infinity Norm
Stefan Kuhlmann, Robert Weismantel
For an integer full column rank matrix , we consider the lattice that consists of all integer combinations of columns of . We prove that a shortest non-zero vector has i…
Sparse Approximation in Lattices and Semigroups
Stefan Kuhlmann, Timm Oertel, Robert Weismantel
This paper deals with the following question: Suppose that there exist an integer or a non-negative integer solution to a system , where the number of non-zero componen…
On Matrices over a Polynomial Ring with Restricted Subdeterminants
Marcel Celaya, Stefan Kuhlmann, Robert Weismantel
This paper introduces a framework to study discrete optimization problems which are parametric in the following sense: their constraint matrices correspond to matrices over the rin…
Integer Carathéodory results with bounded multiplicity
Stefan Kuhlmann
The integer Carathéodory rank of a pointed rational cone is the smallest number such that every integer vector contained in is an integral non-negative combination of a…
Proximity and flatness bounds for linear integer optimization
Marcel Celaya, Stefan Kuhlmann, Joseph Paat +1
We develop a technique that can be applied to provide improved upper bounds for two important questions in linear integer optimization. - Proximity bounds: Given an optimal vertex…
New Bounds for the Integer Carathéodory Rank
Iskander Aliev, Martin Henk, Mark Hogan +2
Given a rational pointed -dimensional cone , we study the integer Carathéodory rank and its asymptotic form , where we co…
Improving the Cook et al. Proximity Bound Given Integral Valued Constraints
Marcel Celaya, Stefan Kuhlmann, Joseph Paat +1
Consider a linear program of the form , where is an integral matrix. In 1986 Cook, Gerards, Schrijver, and Tardos proved that, given an op…
On lattice width of lattice-free polyhedra and height of Hilbert bases
Martin Henk, Stefan Kuhlmann, Robert Weismantel
We study the lattice width of lattice-free polyhedra given by in terms of , the maximal minor in absolute value of $…