DAWN: Matrix Operation-Optimized Algorithm for Shortest Paths Problem on Unweighted Graphs

TL;DR

This paper introduces a matrix operation-optimized algorithm for shortest paths in unweighted graphs that improves parallelism, reduces time complexity, and lowers memory use, outperforming existing BFS methods.

Contribution

The paper presents a novel matrix operation-based algorithm that enhances parallelism and efficiency for shortest path problems in unweighted graphs, addressing limitations of traditional methods.

Findings

Achieved an average speedup of 3.769× over Gunrock BFS.

Achieved an average speedup of 9.410× over GAP BFS.

Reduced memory consumption compared to traditional algorithms.

Abstract

The shortest paths problem is a fundamental challenge in graph theory, with a broad range of potential applications. The algorithms based on matrix multiplication exhibits excellent parallelism and scalability, but is constrained by high memory consumption and algorithmic complexity. Traditional shortest paths algorithms are limited by priority queues, such as BFS and Dijkstra algorithm, making the improvement of their parallelism a focal issue. We propose a matrix operation-optimized algorithm, which offers improved parallelism, reduced time complexity, and lower memory consumption. The novel algorithm requires $O(E_{wcc}(i))$ and $O(S_{wcc} \cdot E_{wcc})$ times for single-source and all-pairs shortest paths problems, respectively, where $S_{wcc}$ and $E_{wcc}$ denote the number of nodes and edges included in the largest weakly connected component in graph. To evaluate the effectiveness of the novel algorithm, we tested it using graphs from SuiteSparse Matrix Collection and Gunrock benchmark dataset. Our algorithm outperformed the BFS implementations from Gunrock and GAP (the previous state-of-the-art solution), achieving an average speedup of 3.769$\times$ and 9.410$\times$, respectively.