Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving Totally Unimodular LPs with the Shadow Vertex Algorithm   We show that the shadow vertex simplex algorithm can be used to solve linear
programs in strongly polynomial time with respect to the number $n$ of
variables, the number $m$ of constraints, and $1/\delta$, where $\delta$ is a
parameter that measures the flatness of the vertices of the polyhedron. This
extends our recent result that the shadow vertex algorithm finds paths of
polynomial length (w.r.t. $n$, $m$, and $1/\delta$) between two given vertices
of a polyhedron.
  Our result also complements a recent result due to Eisenbrand and Vempala who
have shown that a certain version of the random edge pivot rule solves linear
programs with a running time that is strongly polynomial in the number of
variables $n$ and $1/\delta$, but independent of the number $m$ of constraints.
Even though the running time of our algorithm depends on $m$, it is
significantly faster for the important special case of totally unimodular
linear programs, for which $1/\delta\le n$ and which have only $O(n^2)$
constraints.

15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol