@inproceedings{eb91eb4573184cf7ab2059c07fda3f08,

title = "A strongly polynomial algorithm for linear exchange markets",

abstract = "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.",

keywords = "Linear Exchange Markets, Market Equilibria, Strongly Polynomial Algorithm, Z-Matrix",

author = "Jugal Garg and V{\'e}gh, {L{\'a}szl{\'o} A.}",

note = "Publisher Copyright: {\textcopyright} 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.; 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 ; Conference date: 23-06-2019 Through 26-06-2019",

year = "2019",

month = jun,

day = "23",

doi = "10.1145/3313276.3316340",

language = "English (US)",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "54--65",

editor = "Moses Charikar and Edith Cohen",

booktitle = "STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing",

}