EHL*: Memory-Budgeted Indexing for Ultrafast Optimal Euclidean Pathfinding

The Euclidean Shortest Path Problem (ESPP) is a classic problem which requires finding the shortest path in a Euclidean plane with polygonal obstacles. The state-of-the-art solution, Euclidean Hub Labeling (EHL), offers ultra-fast query performance but comes with significant memory overhead, requiring up to tens of gigabytes of storage on large maps, limiting its use in memory-constrained environments like mobile phones. Additionally, EHL's memory usage can only be determined after index construction, and while it provides a memory-runtime tradeoff, it does not fully optimize memory utilization. In this work, we introduce an improved version of EHL, called EHL*, which overcomes these limitations. A key contribution of EHL* is its ability to create an index that adheres to a specified memory budget while optimizing query runtime performance. Moreover, EHL* can leverage pre-known query distributions, a common scenario in many real-world applications, to further enhance runtime efficiency. Our results show that EHL* can reduce memory usage by up to 10-20 times without much impact on query runtime performance compared to EHL, making it a highly effective solution for optimal pathfinding in memory-constrained environments. We also present a theoretical analysis comparing EHL* with EHL, providing insights into their indexing and query processing cost.