A Fast and Efficient Parallel Algorithm for Pruned Landmark Labeling

Hub labeling based shortest distance querying plays a key role in many important networked graph applications, such as route planning, socially-sensitive search and web page ranking. Over the last few years, Pruned Landmark Labeling (PLL) has emerged as the state-of-the-art technique for hub labeling. PLL drastically reduces the complexity of label construction by pruning Shortest-Path Trees (SPTs). However, PLL is inherently sequential, as different SPTs must be constructed in a specific order of source vertices to ensure small label size. Particularly, for large graphs, it takes significant processing time to construct even pruned SPTs from all vertices in the graph. While there are many works on parallelizing single source shortest path, these solutions cannot be directly used for PLL, as pruning and label querying introduce significant additional complexity while restricting parallelism within an SPT. In this paper, we propose a novel, fast and efficient algorithm to significantly accelerate PLL on large graphs based on a two-level parallelization of SPTs: intra- and inter-tree. For intra-tree, we generate pruned SPTs based on a modification of the Bellman-Ford (BF) algorithm. We further optimize BF to reduce SPT label querying and initialization costs. We implement our algorithm using the recently proposed Graph Processing Over Partitions (GPOP) which dramatically improves cache-efficiency and DRAM communication-bandwidth. When pruned SPTs become very small and parallelizing individual SPTs is not advantageous, we switch to inter-tree parallelization and construct multiple trees concurrently in a batch. Experiments conducted on a 36 core (2-way hyperthreaded) Intel Broadwell server show that on some datasets, our proposed parallel algorithm can achieve greater than 35.1× speedup over state-of-the-art sequential algorithm.