A Line Graph-Based Framework for Identifying Optimal Routing Paths in Decentralized Exchanges

ArXiv ID: 2504.15809 “View on arXiv”

Authors: Unknown

Abstract

Decentralized exchanges, such as those employing constant product market makers (CPMMs) like Uniswap V2, play a crucial role in the blockchain ecosystem by enabling peer-to-peer token swaps without intermediaries. Despite the increasing volume of transactions, there remains limited research on identifying optimal trading paths across multiple DEXs. This paper presents a novel line-graph-based algorithm (LG) designed to efficiently discover profitable trading routes within DEX environments. We benchmark LG against the widely adopted Depth-First Search (DFS) algorithm under a linear routing scenario, encompassing platforms such as Uniswap, SushiSwap, and PancakeSwap. Experimental results demonstrate that LG consistently identifies trading paths that are as profitable as, or more profitable than, those found by DFS, while incurring comparable gas costs. Evaluations on Uniswap V2 token graphs across two temporal snapshots further validate LG’s performance. Although LG exhibits exponential runtime growth with respect to graph size in empirical tests, it remains viable for practical, real-world use cases. Our findings underscore the potential of the LG algorithm for industrial adoption, offering tangible benefits to traders and market participants in the DeFi space.

Keywords: Decentralized Exchange (DEX), Constant Product Market Maker, Liquidity Routing, Graph Theory, Gas Optimization, Cryptocurrency (DeFi)

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail
  • Why: The paper presents a novel line-graph algorithm with a theoretical complexity analysis (O(|E| · (P di^2 - 2|E|))) and empirical validation on real DEX data (Uniswap V2, ~200 pools), comparing profitability and gas costs against DFS. It bridges theoretical graph algorithms with practical DeFi applications, demonstrating both advanced mathematics and data-driven results.
  flowchart TD
    A["Research Goal: Identify Optimal Routing Paths in DEXs"] --> B["Data Input: Uniswap V2<br>Token Graphs<br>(Two Temporal Snapshots)"]
    B --> C["Methodology: Line-Graph (LG)<br>vs. Baseline (DFS)"]
    C --> D["Computational Process:<br>Liquidity Routing &<br>Gas Cost Calculation"]
    D --> E["Outcome 1: LG finds paths<br>as profitable or more profitable<br>than DFS"]
    D --> F["Outcome 2: LG incurs<br>comparable gas costs"]
    E --> G["Conclusion: LG viable for<br>industrial adoption in DeFi"]
    F --> G