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Optimal Routing for Constant Function Market Makers

Author

Listed:
  • Guillermo Angeris
  • Tarun Chitra
  • Alex Evans
  • Stephen Boyd

Abstract

We consider the problem of optimally executing an order involving multiple crypto-assets, sometimes called tokens, on a network of multiple constant function market makers (CFMMs). When we ignore the fixed cost associated with executing an order on a CFMM, this optimal routing problem can be cast as a convex optimization problem, which is computationally tractable. When we include the fixed costs, the optimal routing problem is a mixed-integer convex problem, which can be solved using (sometimes slow) global optimization methods, or approximately solved using various heuristics based on convex optimization. The optimal routing problem includes as a special case the problem of identifying an arbitrage present in a network of CFMMs, or certifying that none exists.

Suggested Citation

  • Guillermo Angeris & Tarun Chitra & Alex Evans & Stephen Boyd, 2022. "Optimal Routing for Constant Function Market Makers," Papers 2204.05238, arXiv.org.
    • Handle: RePEc:arx:papers:2204.05238
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    File URL: http://arxiv.org/pdf/2204.05238
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    References listed on IDEAS

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    1. Guillermo Angeris & Akshay Agrawal & Alex Evans & Tarun Chitra & Stephen Boyd, 2021. "Constant Function Market Makers: Multi-Asset Trades via Convex Optimization," Papers 2107.12484, arXiv.org.
    2. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
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    Citations

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    Cited by:

    1. Guillermo Angeris & Tarun Chitra & Theo Diamandis & Alex Evans & Kshitij Kulkarni, 2023. "The Geometry of Constant Function Market Makers," Papers 2308.08066, arXiv.org.
    2. Arman Abgaryan & Utkarsh Sharma, 2023. "Dynamic Function Market Maker," Papers 2307.13624, arXiv.org.
    3. Matheus V. X. Ferreira & David C. Parkes, 2022. "Credible Decentralized Exchange Design via Verifiable Sequencing Rules," Papers 2209.15569, arXiv.org, revised Apr 2023.
    4. Robin Fritsch & Samuel Kaser & Roger Wattenhofer, 2022. "The Economics of Automated Market Makers," Papers 2206.04634, arXiv.org.
    5. Chengqi Zang & Zhenghui Wang & Weitong Zhang, 2026. "A Dynamic Equilibrium Model for Automated Market Makers," Papers 2603.08603, arXiv.org.
    6. Matthew Willetts & Christian Harrington, 2026. "Pools as Portfolios: Observed arbitrage efficiency & LVR analysis of dynamic weight AMMs," Papers 2602.22069, arXiv.org.
    7. Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    8. Estelle Sterrett & Waylon Jepsen & Evan Kim, 2022. "Replicating Portfolios: Constructing Permissionless Derivatives," Papers 2205.09890, arXiv.org, revised Jun 2022.
    9. Sebastian Jaimungal & Yuri F. Saporito & Max O. Souza & Yuri Thamsten, 2023. "Optimal Trading in Automatic Market Makers with Deep Learning," Papers 2304.02180, arXiv.org.
    10. Stefan Loesch & Mark Bentley Richardson, 2025. "Marginal Price Optimization," Papers 2502.08258, arXiv.org.
    11. Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.
    12. Carlos Escudero & Felipe Lara & Miguel Sama, 2026. "Optimal Routing across Constant Function Market Makers with Gas Fees," Papers 2603.02844, arXiv.org.
    13. Kshitij Kulkarni & Theo Diamandis & Tarun Chitra, 2022. "Towards a Theory of Maximal Extractable Value I: Constant Function Market Makers," Papers 2207.11835, arXiv.org, revised Apr 2023.

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