SlimSell: A Vectorizable Graph Representation for Breadth-First Search

TL;DR

This paper introduces SlimSell, a vectorizable graph representation designed to accelerate BFS on modern architectures by leveraging SIMD-friendly storage formats and semiring operations, achieving significant speedups.

Contribution

SlimSell extends existing matrix storage formats with new semiring operations and load balancing schemes to improve BFS performance on diverse hardware.

Findings

Achieves up to 33% speedup on Graph500 BFS code.

Reduces storage requirements by up to 50%.

Demonstrates effectiveness across CPUs, KNL, and GPUs.

Abstract

Vectorization and GPUs will profoundly change graph processing. Traditional graph algorithms tuned for 32- or 64-bit based memory accesses will be inefficient on architectures with 512-bit wide (or larger) instruction units that are already present in the Intel Knights Landing (KNL) manycore CPU. Anticipating this shift, we propose SlimSell: a vectorizable graph representation to accelerate Breadth-First Search (BFS) based on sparse-matrix dense-vector (SpMV) products. SlimSell extends and combines the state-of-the-art SIMD-friendly Sell-C-sigma matrix storage format with tropical, real, boolean, and sel-max semiring operations. The resulting design reduces the necessary storage (by up to 50%) and thus pressure on the memory subsystem. We augment SlimSell with the SlimWork and SlimChunk schemes that reduce the amount of work and improve load balance, further accelerating BFS. We evaluate all the schemes on Intel Haswell multicore CPUs, the state-of-the-art Intel Xeon Phi KNL manycore CPUs, and NVIDIA Tesla GPUs. Our experiments indicate which semiring offers highest speedups for BFS and illustrate that SlimSell accelerates a tuned Graph500 BFS code by up to 33%. This work shows that vectorization can secure high-performance in BFS based on SpMV products; the proposed principles and designs can be extended to other graph algorithms.