Parallel Contraction Hierarchies Can Be Efficient and Scalable

TL;DR

This paper introduces SPoCH, a new parallel algorithm for constructing contraction hierarchies that significantly reduces build time while maintaining query efficiency, outperforming existing methods on various graph datasets.

Contribution

The paper presents SPoCH, a scalable parallel algorithm for contraction hierarchy construction that improves speedup and scalability over prior solutions.

Findings

SPoCH achieves 11 to 68 times speedup over sequential algorithms.

SPoCH outperforms existing parallel solutions by 3.8 to 41 times.

The method maintains competitive query performance and graph size.

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 performance close to sequential algorithms. 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. We compare SPoCH with the state-of-the-art sequential and parallel implementations on 16 graphs of various types. Our experiments show that SPoCH achieves speedups of 11 to 68 times over the best sequential baseline and 3.8 to 41 times over the best parallel baseline in CH construction, while maintaining competitive query performance and CH graph size. We have released our code and all datasets used in this paper.