Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

Abstract

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory.This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 13 important graph problems. We also present the optimizations and techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We provide a publicly-available benchmark suite containing our implementations.

High-Performance Parallel Graph Coloring with Strong Guarantees on Work, Depth, and Quality

“…Algorithms & Comparison Baselines We focus on modern heuristics from Table III. For each scheme, we always pick the most competitive implementation (i.e., fewest colors used and smallest performance overheads), selecting from existing repositories, illustrated in Table IV (ColPack [82], [90], Zoltan [35], [91]- [94], original code by Hasenplaugh et al (HP) [31], GBBS with Ligra [61], [95], [96]), and our implementation. Detailed parametrizations are in the reproducibility appendix.…”

“…Following related work [31], [61], we assume that a parallel computation (modeled as a DAG) runs on the ideal parallel computer (machine model). Each instruction executes in unit time and there is support for concurrent reads, writes, and read-modify-write atomics (any number of such instructions finish in O(1) time).…”

“…Each instruction executes in unit time and there is support for concurrent reads, writes, and read-modify-write atomics (any number of such instructions finish in O(1) time). These are standard assumptions used in all recent parallel graph coloring algorithms [31], [61]. We develop algorithms based on these assumptions but we also provide algorithms that use weaker assumptions (algorithms that only rely on concurrent reads).…”

“…We integrated our algorithms with both the GAP benchmark suite [87] and with GBBS [61], a recent platform for testing parallel graph algorithms. We use OpenMP [88] for parallelization.…”

“…(MIS) Luby [30] ColPack Gebremedhin [37] ColPack Gebremedhin [37] ColPack ITRB (Boman et al [38] Zoltan ITR (C ¸ataly ürek et al [40] and others [43], [45]) ColPack ITR-ASL (Patwary et al [32]) ColPack Greedy-ID [1] ColPack, GBBS Greedy-SD [27], [31] ColPack, GBBS JP-FF [25], [31] ColPack, GBBS JP-LF [31] ColPack, GBBS, HP JP-SL [31] ColPack, GBBS, HP JP-R [26] ColPack, GBBS, HP JP-R [31] ColPack, GBBS, HP JP-LLF [31] GBBS, HP JP-SLL [31] GBBS, HP JP-ASL [32], [82] ColPack [31], and GBBS with Ligra [61], [95], [96].…”