The Breadth-First Search (BFS) algorithm is an important building block for graph analysis of large datasets. The BFS parallelisation has been shown to be challenging because of its inherent characteristics, including irregular memory access patterns, data dependencies and workload imbalance, that limit its scalability. We investigate the optimisation and vectorisation of the hybrid BFS (a combination of top-down and bottom-up approaches for BFS) on the Xeon Phi, which has advanced vector processing capabilities. The results show that our new implementation improves by 33%, for a one million vertices graph, compared to the state-of-the-art.

Breadth First Search (BFS) is a building block for graph algorithms and has recently been used for large scale analysis of information in a variety of applications including social networks, graph databases and web searching. Due to its importance, a number of different parallel programming models and architectures have been exploited to optimize the BFS. However, due to the irregular memory access patterns and the unstructured nature of the large graphs, its efficient parallelization is a challenge. The Xeon Phi is a massively parallel architecture available as an off-the-shelf accelerator, which includes a powerful 512 bit vector unit with optimized scatter and gather functions. Given its potential benefits, work related to graph traversing on this architecture is an active area of research.We present a set of experiments in which we explore architectural features of the Xeon Phi and how best to exploit them in a top-down BFS algorithm but the techniques can be applied to the current state-of-the-art hybrid, top-down plus bottom-up, algorithms.We focus on the exploitation of the vector unit by developing an improved highly vectorized OpenMP parallel algorithm, using vector intrinsics, and understanding the use of data alignment and prefetching. In addition, we investigate the impact of hyperthreading and thread affinity on performance, a topic that appears under researched in the literature. As a result, we achieve what we believe is the fastest published top-down BFS algorithm on the version of Xeon Phi used in our experiments. The vectorized BFS topdown source code presented in this paper can be available on request as free-to-use software.

Modern applications generate massive amounts of data that is challenging to process or analyse. Graph algorithms have emerged as a solution for the analysis of such data because they can represent the entities participating in the generation of large-scale datasets in terms of vertices and their relationships in terms of edges. Graph analysis algorithms are used for finding patterns within these relationships, aiming to extract information to be further analysed. The breadth-first search (BFS) is one of the main graph search algorithms used for graph analysis and its optimisation has been widely researched using different parallel computers. However, the parallelisation of BFS has been shown to be challenging because of its inherent characteristics, including irregular memory access patterns, data dependencies and workload imbalance, that limit its scalability. This paper investigates the optimisation of the BFS on the Xeon Phi (Knights Corner), a modern parallel architecture provided with an advanced vector processor supporting the AVX-512 instruction set, using a bespoke development framework integrated with the Graph 500 benchmark. In addition, to demonstrate portability, we show results for a direct port of the algorithms to a more recent version of the Xeon Phi (Knights Landing) and to a Skylake CPU which supports most of the AVX-512 instruction set. Optimised parallel versions of two high-level algorithms for BFS were created using vectorisation, starting with the conventional top-down BFS algorithm and, building on this, a hybrid BFS algorithm. On the KNC our best implementations result in speedups of 1.37x (top-down) and 1.37x (hybrid), for a one million vertices graph, compared to the state-of-the-art. On the KNL and Skylake, the performance is higher than on KNC. In addition, we show results of our best hybrid algorithm on real-world graphs from the SNAP datasets with speedups up to 1.3x on KNC. Performance on KNL and Skylake is again higher, demonstrating the robustness and portability of our algorithm. The hybrid BFS algorithm can be further used to speed up other graph analysis algorithms and the lessons learned from vectorisation can be applied to other algorithms targeting existing and future models of the Xeon Phi and other advanced vector architectures.

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