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

TL;DR

This work tackles the Euclidean Shortest Path Problem by improving the state-of-the-art Euclidean Hub Labeling (EHL) with EHL*, a memory-budgeted variant. EHL* introduces a compression phase that merges adjacent grid cells into regional regions to fit a user-defined memory budget $\mathcal{B}$ while preserving optimal distances, and it can exploit known query distributions to further optimize runtime. Empirical results show EHL* can reduce memory usage by up to 10-20x with minimal runtime penalties, and when query distributions are known, it can surpass EHL in both memory efficiency and query speed. The approach offers a practical pathway for memory-constrained environments and real-world workloads, with future work pointing toward machine-learning-driven region selection for further improvements.

Abstract

The Euclidean Shortest Path Problem (ESPP), which involves finding the shortest path in a Euclidean plane with polygonal obstacles, is a classic problem with numerous real-world applications. The current state-of-the-art solution, Euclidean Hub Labeling (EHL), offers ultra-fast query performance, outperforming existing techniques by 1-2 orders of magnitude in runtime efficiency. However, this performance comes at the cost of significant memory overhead, requiring up to tens of gigabytes of storage on large maps, which can limit its applicability in memory-constrained environments like mobile phones or smaller devices. 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 preknown 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.

Figures (5)

• Figure 1: Memory-runtime tradeoff provided by EHL and EHL* on the Expedition map.
• Figure 2: Visibility graph for the example in Figure \ref{['fig::running_example']}
• Figure 3: Euclidean plane with polygonal obstacles
• Figure 4: Grid cell $c_s$ with its adjacent neighbors
• Figure 5: Distribution of merged grids for arena map for different cluster scenarios at 5% memory. The red rectangles represents the cluster regions generated in the arena map. Black polygons are the obstacles.

Theorems & Definitions (4)

• Example 1
• Example 2
• Example 3
• Example 4