6 citations · 6 across the 2 of their papers we have counts for
7 papers
Optimizing Sparsity over Lattices and Semigroups
Iskander Aliev, Gennadiy Averkov, Jesús A. De Loera +1
Motivated by problems in optimization we study the sparsity of the solutions to systems of linear Diophantine equations and linear integer programs, i.e., the number of non-zero en…
Sparsity of integer solutions in the average case
Timm Oertel, Joseph Paat, Robert Weismantel
We examine how sparse feasible solutions of integer programs are, on average. Average case here means that we fix the constraint matrix and vary the right-hand side vectors. For a…
The distributions of functions related to parametric integer optimization
Timm Oertel, Joseph Paat, Robert Weismantel
We consider the asymptotic distribution of the IP sparsity function, which measures the minimal support of optimal IP solutions, and the IP to LP distance function, which measures…
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…
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…