Paper: arXiv 2302.04938

Authors: Theo Diamandis, Max Resnick, Tarun Chitra, Guillermo Angeris

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.0/10 (capped from 7.0: no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper provides a highly rigorous mathematical formulation of optimal trade routing across Constant Function Market Maker (CFMM) networks using convex optimization and decomposition techniques. It bridges theoretical financial engineering with strong empirical benchmarks against state-of-the-art commercial solvers.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Trade Routing Across CFMM Networks] --> B[Inputs: User Utility Function & CFMM Liquidity Pools]
    B --> C[Formulate Convex Optimization Problem]
    C --> D[Apply Operator Splitting Decomposition Method]
    D --> E[Benchmark vs. Off-the-Shelf Commercial Solver]
    E --> F[Outcome: Fast Algorithm Supporting Complex CFMMs like Uniswap v3]
    E --> G[Outcome: Significant Performance Improvements in Execution Speed]