34 citations · 53 across the 24 of their papers we have counts for
30 papers
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…
Minkowski's successive minima in convex and discrete geometry
Iskander Aliev, Martin Henk
In this short survey we want to present some of the impact of Minkowski's successive minima within Convex and Discrete Geometry. Originally related to the volume of an -symmetri…
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…
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…
On the volume of hyperplane sections of a d-cube
Iskander Aliev
We obtain an optimal upper bound for the normalised volume of a hyperplane section of an origin-symmetric d-dimensional cube. This confirms a conjecture posed by Imre Barany and Pe…