An Efficient Algorithm for Optimal Routing Through Constant Function Market Makers

TL;DR

This paper introduces an efficient decomposition-based algorithm for optimal trade routing across networks of constant function market makers, improving performance over existing solvers and accommodating complex CFMMs like Uniswap v3.

Contribution

The paper presents a novel decomposition algorithm that efficiently solves the optimal routing problem across CFMM networks, including complex variants like Uniswap v3.

Findings

Significant performance improvements over commercial solvers.

Effective incorporation of complex CFMMs into routing.

Validated on realistic CFMM networks.

Abstract

Constant function market makers (CFMMs) such as Uniswap have facilitated trillions of dollars of digital asset trades and have billions of dollars of liquidity. One natural question is how to optimally route trades across a network of CFMMs in order to ensure the largest possible utility (as specified by a user). We present an efficient algorithm, based on a decomposition method, to solve the problem of optimally executing an order across a network of decentralized exchanges. The decomposition method, as a side effect, makes it simple to incorporate more complicated CFMMs, or even include 'aggregate CFMMs' (such as Uniswap v3), into the routing problem. Numerical results show significant performance improvements of this method, tested on realistic networks of CFMMs, when compared against an off-the-shelf commercial solver.