Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Graver Complexity of Integer Programming   In this article we establish an exponential lower bound on the Graver
complexity of integer programs. This provides new type of evidence supporting
the presumable intractability of integer programming. Specifically, we show
that the Graver complexity of the incidence matrix of the complete bipartite
graph $K_{3,m}$ satisfies $g(m)=\Omega(2^m)$, with $g(m)\geq 17\cdot 2^{m-3}-7$
for every $m>3$ .

3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas