### Authors

Tarun Chitra, Theo Diamandis, Max Resnick, Guillermo Angeris

February 1, 2023

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# An Efficient Algorithm for Optimal Routing Through Constant Function Market Makers

### Key Takeaways

A natural question for constant function market makers is how to optimally route trades across a network of them in order to ensure the largest possible utility (as specified by a user).

This paper presents an efficient algorithm, based on a decomposition method, to solve the problem of optimally executing an order across a network of decentralized exchanges.

Numerical results show significant performance improvements of this method, tested on realistic networks of CFMMs, when compared against an off-the-shelf commercial solver.

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