On-chain optimal aggregation of Uniswap v3 clones

Vincent Danos (), Leo Watson, Hamza El Khalloufi () and Santiago Valencia
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Vincent Danos: DI-ENS - Département d'informatique - ENS-PSL - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique
Leo Watson: University of Toronto
Hamza El Khalloufi: UP1 - Université Paris 1 Panthéon-Sorbonne

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Abstract: In this paper we define a simple and efficient "push-and-solve" algorithm to compute the best execution or "optimal split" of a market order given a finite set of AMMs. Each AMM has to be decomposable into basic building blocks which we call price-parametrised AMMs. This has a practical application to the optimal splitting of orders among Uniswap v3 clones, as the algorithm is query-optimal (information on sources is queried on a call-by-need basis) and therefore of low enough complexity to be implemented as a smart contract. We also find a sufficient condition for AMMs based on price parametrisations to be aggregatable which is of independent interest as it allows one to build novel AMMs with concentrated liquidity, families of which can also be optimally executed on-chain.

Date: 2024-11-22
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