Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distances of optimal solutions of mixed-integer programs   A classic result of Cook et al. (1986) bounds the distances between optimal
solutions of mixed-integer linear programs and optimal solutions of the
corresponding linear relaxations. Their bound is given in terms of the number
of variables and a parameter $ \Delta $, which quantifies sub-determinants of
the underlying linear inequalities. We show that this distance can be bounded
in terms of $ \Delta $ and the number of integer variables rather than the
total number of variables. To this end, we make use of a result by Olson (1969)
in additive combinatorics and demonstrate how it implies feasibility of certain
mixed-integer linear programs. We conjecture that our bound can be improved to
a function that only depends on $ \Delta $, in general.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin