Measuring DEX Efficiency and The Effect of an Enhanced Routing Method on Both DEX Efficiency and Stakeholders’ Benefits

ArXiv ID: 2508.03217 “View on arXiv”

Authors: Yu Zhang, Claudio J. Tessone

Abstract

The efficiency of decentralized exchanges (DEXs) and the influence of token routing algorithms on market performance and stakeholder outcomes remain underexplored. This paper introduces the concept of Standardized Total Arbitrage Profit (STAP), computed via convex optimization, as a systematic measure of DEX efficiency. We prove that executing the trade order maximizing STAP and reintegrating the resulting transaction fees eliminates all arbitrage opportunities-both cyclic arbitrage within DEXs and between DEXs and centralized exchanges (CEXs). In a fully efficient DEX (i.e., STAP = 0), the monetary value of target tokens received must not exceed that of the source tokens, regardless of the routing algorithm. Any violation indicates arbitrage potential, making STAP a reliable metric for arbitrage detection. Using a token graph comprising 11 tokens and 18 liquidity pools based on Uniswap V2 data, we observe a decline in DEX efficiency between June 21 and November 8, 2024. Simulations comparing two routing algorithms-Yu Zhang et al.’s line-graph-based method and the depth-first search (DFS) algorithm-show that employing more profitable routing improves DEX efficiency and trader returns over time. Moreover, while total value locked (TVL) remains stable with the line-graph method, it increases under the DFS algorithm, indicating greater aggregate benefits for liquidity providers.

Keywords: Decentralized Exchange (DEX), Arbitrage Profit (STAP), Convex Optimization, Routing Algorithms, Liquidity Pools, Cryptocurrencies

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail
  • Why: The paper introduces advanced convex optimization concepts (Standardized Total Arbitrage Profit) with mathematical proofs, demonstrating high math density. It also employs empirical methods with a specific token graph, Uniswap V2 data spanning six months, and simulations comparing routing algorithms, resulting in high implementation and backtest readiness.
  flowchart TD
    A["Research Goal:<br>Measure DEX Efficiency &<br>Assess Routing Algorithms"] --> B["Methodology:<br>Compute STAP<br>(Standardized Total Arbitrage Profit)<br>via Convex Optimization"]
    B --> C["Data/Inputs:<br>11 Tokens, 18 Liquidity Pools<br>(Uniswap V2)"]
    C --> D["Computational Process:<br>Simulate Trades &<br>Compare Routing Algorithms<br>(Line-Graph vs. DFS)"]
    D --> E{"Analysis of<br>Outcomes"}
    E --> F["Key Finding 1:<br>STAP = 0 implies DEX Efficiency<br>STAP > 0 implies Arbitrage"]
    E --> G["Key Finding 2:<br>More Profitable Routing<br>(DFS) improves Efficiency,<br>Trader Returns, & TVL"]