Locality-Based Relaxation: An Efficient Method for GPU-Based Computation of Shortest Paths

Abstract

This paper presents a novel parallel algorithm for solving the Single-Source Shortest Path (SSSP) problem on GPUs. The proposed algorithm is based on the idea of locality-based relaxation, where instead of updating just the distance of a single vertex v, we update the distances of v's neighboring vertices up to k steps. The proposed algorithm also implements a communication-efficient method (in the CUDA programming model) that minimizes the number of kernel launches, the number of atomic operations and the frequency of CPU-GPU communication without any need for thread synchronization. This is a significant contribution as most existing methods often minimize one at the expense of another. Our experimental results demonstrate that our approach outperforms most existing methods on real-world road networks of up to 6.3 million vertices and 15 million arcs (on weaker GPUs).

Automated Verification of the Parallel Bellman–Ford Algorithm

“…In this paper, we prove race freedom, memory safety and functional correctness of a standard parallel GPU-based Bellman-Ford algorithm. This correctness proof can be used as a starting point to also derive correctness of the various optimized implementations that have been proposed in the literature [1,9,18,20,32,34]. Moreover, this work and the experiences with automated reasoning about GPU-based graph algorithms will also provide a good starting point to verify other parallel GPU-based graph algorithms.…”