Fast and Efficient Parallel Breadth-First Search with Power-law Graph Transformation

TL;DR

The paper tackles the challenge of efficient BFS on large, skewed graphs by combining Reverse Cuthill-Mckee (RCM) reordering with a hybrid level-synchronous/top-down and bottom-up BFS on an ARMv8 platform, augmented by NEON SIMD optimizations. The approach improves data locality, reduces cache misses, and enables dynamic load balancing and workload reduction during the bottom-up phase, achieving strong scalability and substantial speedups. Key contributions include the RCM-based graph relabeling with isolated vertices excluded, a detailed load-balancing strategy for the top-down phase, bottom-up workload reduction via bitmap frontiers and work-stealing, and SIMD acceleration; these are validated on Graph500 Kronecker graphs and real-world networks. The results demonstrate significant performance gains, including near-linear strong scaling and a Green Graph500 rank, underscoring the practical potential for faster traversal-based graph algorithms on CPU+SIMD architectures.

Abstract

In the big data era, graph computing is widely used to exploit the hidden value in real-world graphs in various scenarios such as social networks, knowledge graphs, web searching, and recommendation systems. However, the random memory accesses result in inefficient use of cache and the irregular degree distribution leads to substantial load imbalance. Breadth-First Search (BFS) is frequently utilized as a kernel for many important and complex graph algorithms. In this paper, we describe a preprocessing approach using Reverse Cuthill-Mckee (RCM) algorithm to improve data locality and demonstrate how to achieve an efficient load balancing for BFS. Computations on RCM-reordered graph data are also accelerated with SIMD executions. We evaluate the performance of the graph preprocessing approach on Kronecker graphs of the Graph500 benchmark and real-world graphs. Our BFS implementation on RCM-reordered graph data achieves 326.48 MTEPS/W (mega TEPS per watt) on an ARMv8 system, ranking 2nd on the Green Graph500 list in June 2020 (the 1st rank uses GPU acceleration).

Figures (5)

• Figure 1: Structure comparison of adjacency matrices before and after RCM-reordering. The left side shows the adjacency matrix for the original Kronecker graph. The right side shows the adjacency matrix for the RCM-reordered graph.
• Figure 2: Comparison of distribution of edges among threads in a top-down step (scale 26, edgefactor 16, level 3). The edges are nearly evenly distributed to each thread for Alg. 4. However, for Alg. 1, most edges are assigned to the first several threads.
• Figure 3: Size of all partitions at each bottom-up step before and after RCM-reordering. Each size is the average of values collected from the 64 rounds BFS (40 threads, edgefactor 16, $\lambda$ 20). The initial size of all partitions for the RCM-reordered graph is smaller than that of the original Kronecker graph because all isolated vertices are excluded. The former shows a significant reduction for all scales while the latter rarely reduces when the scale is greater than 24.
• Figure 4: Ablation experiments on different optimizations. 1. baseline: hybrid bfs; 2.rmv-iso: baseline + remove isolated vertices; 3.RCM: rmv-iso +RCM; 4.rcm-lb: RCM+load balance; 5.rcm-simd: rcm-lb + simd.
• Figure 5: Partial RCM on Kronecker, twitter and friendster graphs.