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

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons127643

Duan,  Ran
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons134167

Garg,  Jugal
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Duan, R., Garg, J., & Mehlhorn, K. (2016). An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market. In R. Krauthgamer (Ed.), Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 90-106). Philadelphia, PA: SIAM. doi:10.1137/1.9781611974331.ch7.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0028-81DD-9
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 $O(n^7 \log^3 (nU))$ time. This improves upon the previously best algorithm of Ye by a factor of $\tOmega(n)$. The algorithm refines the algorithm described by Duan and Mehlhorn and improves it by a factor of $\tOmega(n^3)$. 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.