34 citations · 53 across the 24 of their papers we have counts for
4 papers · 1 filter
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…
Distances to Lattice Points in Knapsack Polyhedra
Iskander Aliev, Martin Henk, Timm Oertel
We give an optimal upper bound for the maximum-norm distance from a vertex of a knapsack polyhedron to its nearest feasible lattice point. In a randomised setting, we show that the…
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…
Integer Points in Knapsack Polytopes and s-covering Radius
Iskander Aliev, Martin Henk, Eva Linke
Given an integer matrix A satisfying certain regularity assumptions, we consider for a positive integer s the set F_s(A) of all integer vectors b such that the associated knapsack…