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On the Implementation of Combinatorial Algorithms for the Linear Exchange Market

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Algorithms, Probability, Networks, and Games

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9295))

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Abstract

Duan and Mehlhorn and Duan, Garg, and Mehlhorn presented polynomial time combinatorial algorithms [DM13, DGM15] for the computation of equilibrium prices in linear exchange markets. I am currently implementing these algorithms. I discuss the questions that I hope to answer through the implementation.

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Notes

  1. 1.

    Clearly \(b_1 \ge |r(B)|/n\). Also, \({r(b_j)}/{r(b_{j+1})}\le 1+1/n\) for \(j<\ell \), and hence \(r(b_\ell )\ge r(b_1)/(1+1/n)^{-n} \ge r(b_1)/e \ge |r(B)|/(e \cdot n)\).

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Author information

Authors and Affiliations

  1. Max-Planck-Institute for Informatics, Saarbrücken, Germany

    Kurt Mehlhorn

Authors
  1. Kurt Mehlhorn
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Correspondence to Kurt Mehlhorn .

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Editors and Affiliations

  1. University of Patras, Patras, Greece

    Christos Zaroliagis

  2. Technological Educational Institute of Athens, Athens, Greece

    Grammati Pantziou

  3. University of Ioannina, Ioannina, Greece

    Spyros Kontogiannis

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Mehlhorn, K. (2015). On the Implementation of Combinatorial Algorithms for the Linear Exchange Market. In: Zaroliagis, C., Pantziou, G., Kontogiannis, S. (eds) Algorithms, Probability, Networks, and Games. Lecture Notes in Computer Science(), vol 9295. Springer, Cham. https://doi.org/10.1007/978-3-319-24024-4_7

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  • DOI: https://doi.org/10.1007/978-3-319-24024-4_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24023-7

  • Online ISBN: 978-3-319-24024-4

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