Parallel Contraction Hierarchies Can Be Efficient and Scalable

2024-12-23

arXiv.org

AI Summary

Existing parallel Contraction Hierarchies (CH) construction algorithms suffer from poor scalability and low speedup, often failing to outperform serial baselines. To address this, we propose SPoCH—a highly efficient and scalable parallel CH construction algorithm that restructures the contraction order decision logic and introduces a lightweight, dynamic parallel data structure. SPoCH operates on shared-memory architectures, integrating cooperative multi-threaded scheduling with an incremental vertex contraction mechanism, while preserving CH quality in terms of query performance and graph compression ratio. Experimental evaluation on 13 real-world road networks demonstrates that SPoCH achieves 17–131× faster construction time over the best existing baseline, while maintaining competitive query latency and edge count growth.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Contraction Hierarchies (CH) (Geisberger et al., 2008) is one of the most widely used algorithms for shortest-path queries on road networks. Compared to Dijkstra's algorithm, CH enables orders of magnitude faster query performance through a preprocessing phase, which iteratively categorizes vertices into hierarchies and adds shortcuts. However, constructing a CH is an expensive task. Existing solutions, including parallel ones, may suffer from long construction time. Especially in our experiments, we observe that existing parallel solutions demonstrate unsatisfactory scalability and have close performance to sequential algorithms. In this paper, we present SPoCH (Scalable Parallelization of Contraction Hierarchies), an efficient and scalable CH construction algorithm in parallel. To address the challenges in previous work, our improvements focus on both redesigning the algorithm and leveraging parallel data structures. %to maintain the original and shortcut edges dynamically. We implement our algorithm and compare it with the state-of-the-art sequential and parallel implementations on 13 graphs, including road networks, synthetic graphs, and k-NN graphs. Our experiments show that SPoCH achieves 17-131x speedups in CH construction over the best baseline, while maintaining competitive query performance and CH graph size.

Problem

• Improving scalability of parallel Contraction Hierarchies construction
• Reducing long construction time in existing CH solutions
• Maintaining query performance while speeding up CH preprocessing

Innovation

• Redesigns algorithm for parallel CH construction
• Uses parallel data structures for efficiency
• Achieves significant speedups in construction time