34 citations · 53 across the 24 of their papers we have counts for
11 papers · 1 filter
Optimal Proximity Bound and Product Function Estimates in Integer Linear Programming
Iskander Aliev, Gennadiy Averkov, William Jones +1
We obtain an optimal proximity bound for integer linear programs in standard form max{cx: Ax=b, x nonnegative integer}, where A is an integer mxn matrix of rank m<n and b is an int…
Sparsity and integrality gap transference bounds for integer programs
Iskander Aliev, Marcel Celaya, Martin Henk
We obtain new transference bounds that connect two active areas of research: proximity and sparsity of solutions to integer programs. Specifically, we study the additive integralit…
Distance-sparsity transference for vertices of corner polyhedra
Iskander Aliev, Marcel Celaya, Martin Henk +1
We obtain a transference bound for vertices of corner polyhedra that connects two well-established areas of research: proximity and sparsity of solutions to integer programs. In th…
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…
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{…
Integrality Gaps of Integer Knapsack Problems
Iskander Aliev, Martin Henk, Timm Oertel
We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a "typical"…