# Optimal Routing for Constant Function Market Makers

arXiv: https://arxiv.org/abs/2204.05238 · HTML: https://mlsanity.com/paper/2204.05238/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2022.

## Built on by (most cited first, 3 of 3)

- [Explainable AI via Learning to Optimize](https://mlsanity.com/paper/2204.14174/) (2022)
- [Cooperative AI via Decentralized Commitment Devices](https://mlsanity.com/paper/2311.07815/) (2023)
- [SAiFE-gym: Model-based Environments for Automated Market Making with Concentrated Liquidity](https://mlsanity.com/paper/2609.17788/) (2026)

## Abstract (arXiv)

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.