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

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.