An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market

Ran Duan, Jugal Garg, Kurt Mehlhorn

Abstract: We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with n agents and integral utilities bounded by U, the algorithm runs in O(n7 log3(nU)) time. This improves upon the previously best algorithm of Ye by a factor of . The algorithm refines the algorithm described by Duan and Mehlhorn and improves it by a factor of . The improvement comes from a better understanding of the iterative price adjustment process, the improved balanced flow computation for nondegenerate instances, and a novel perturbation technique for achieving nondegeneracy.