We refer to the distance between optimal solutions of integer programs and their linear
relaxations as proximity. In 2018 Eisenbrand and Weismantel proved that proximity is …

Consider a linear program of the form max {c⊤ x: A x≤ b}, where A is an m× n integral
matrix. In 1986 Cook, Gerards, Schrijver, and Tardos proved that, given an optimal solution …

The Steinitz constant in dimension d is the smallest value c (d) such that for any norm on R d
and for any finite zero-sum sequence in the unit ball, the sequence can be permuted such …

Many papers in the field of integer linear programming (ILP, for short) are devoted to
problems of the type max {c⊤ x: A x= b, x∈ Z≥ 0 n}, where all the entries of A, b, c are …

We consider the asymptotic distribution of the integer program (IP) sparsity function, which
measures the minimal support of optimal IP solutions, and the IP to linear program (LP) …

We introduce a general random model of a combinatorial optimization problem with
geometric structure that encapsulates both linear programming and integer linear …

This paper deals with linear integer optimization. We develop a technique that can be
applied to provide improved upper bounds for two important questions in linear integer …

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 the …

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 …

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 integrality gap of …