Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Strongly Polynomial Algorithm for Linear Exchange Markets   We present a strongly polynomial algorithm for computing an equilibrium in
Arrow-Debreu exchange markets with linear utilities. Our algorithm is based on
a variant of the weakly-polynomial Duan-Mehlhorn (DM) algorithm. We use the DM
algorithm as a subroutine to identify revealed edges, i.e. pairs of agents and
goods that must correspond to best bang-per-buck transactions in every
equilibrium solution. Every time a new revealed edge is found, we use another
subroutine that decides if there is an optimal solution using the current set
of revealed edges, or if none exists, finds the solution that approximately
minimizes the violation of the demand and supply constraints. This task can be
reduced to solving a linear program (LP). Even though we are unable to solve
this LP in strongly polynomial time, we show that it can be approximated by a
simpler LP with two variables per inequality that is solvable in strongly
polynomial time.

9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga