ALBBA: An efficient ALgebraic Bypass BFS Algorithm on long vector architectures

Breadth First Search (BFS) is a fundamental algorithm in scientific computing, databases, and network analysis applications. In the algebraic BFS paradigm, each BFS iteration is expressed as a sparse matrix–vector multiplication, allowing BFS to be accelerated and analyzed through well-established linear algebra primitives. Although much effort has been made to optimize algebraic BFS on parallel platforms such as CPUs, GPUs, and distributed memory systems, vector architectures that exploit Single Instruction Multiple Data (SIMD) parallelism, particularly with their high performance on sparse workloads, remain relatively underexplored for BFS.

In this paper, we propose the ALgebraic Bypass BFS Algorithm (ALBBA), a novel and efficient algebraic BFS implementation optimized for long vector architectures. ALBBA utilizes a customized variant of the SELL-$C$-$\sigma$ data structure to fully exploit the SIMD capabilities. By integrating a vectorization-friendly search method alongside a two-level bypass strategy, we enhance both sparse matrix-sparse vector multiplication (SpMSpV) and sparse matrix-dense vector multiplication (SpMV) algorithms, which are crucial for algebraic BFS operations. We further incorporate merge primitives and adopt an efficient selection method for each BFS iteration. Our experiments on an NEC VE20B processor demonstrate that ALBBA achieves average speedups of 3.91$\times$ , 2.88$\times$ , and 1.46$\times$ over Enterprise, GraphBLAST, and Gunrock running on an NVIDIA H100 GPU, respectively.