Comprehensive Evaluation of a New GPU-based Approach to the Shortest Path Problem

Abstract

The Single-Source Shortest Path (SSSP) problem arises in many different fields. In this paper, we present a GPU SSSP algorithm implementation. Our work significantly speeds up the computation of the SSSP, not only with respect to a CPU-based version, but also to other state-of-the-art GPU implementations based on Dijkstra. Both GPU implementations have been evaluated using the latest NVIDIA architectures. The graphs chosen as input sets vary in nature, size, and fan-out degree, in order to evaluate the behavior of the algorithms for different data classes. Additionally, we have enhanced our GPU algorithm implementation using two optimization techniques: The use of a proper choice of threadblock size; and the modification of the GPU L1 cache memory state of NVIDIA devices. These optimizations lead to performance improvements of up to 23% with respect to the non-optimized versions. In addition, we have made a platform comparison of several NVIDIA boards in order to distinguish which one is better for each class of graphs, depending on their features. Finally, we compare our results with an optimized sequential implementation of Dijkstra's algorithm included in the reference Boost library, obtaining an improvement ratio of up to 19× for some graph families, using less memory space.

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

“…As such, we would like to minimize the number of atomic statements. In addition to our algorithm and Harish et al's [12,13], Singh et al [26], Chaibou et al [6] and Ortega et al [20,21] present algorithms with just one atomic statement. Chaibou et al [6] evaluate the cost of memory copy between CPU and GPU.…”

“…Chaibou et al [6] evaluate the cost of memory copy between CPU and GPU. Ortega et al [20,21] propose an algorithm based on Dijkstra's algorithm to find SSSP. Their method extends Martin et al's [17] and Crauser et al's [7].…”

“…Their idea is based on maximizing the number of relaxations in each iteration while preserving the correctness of Dijkstra's algorithm. Ortega et al [20,21] implement these two ideas on GPUs. Nasre et al [19] claim that atomic-free algorithms perform more efficiently than the algorithms that use atomic statements.…”

Trajectory planning for UAV navigation in dynamic environments with matrix alignment Dijkstra

“…For different application scenarios, the variants of Dijkstra and A* [15] [16] [17] [18]have been proposed. Many researchers have introduced some parallel algorithms [13] [14] with improved efficiency. The differential evolution (DE) algorithm is another efficient random search algorithm to deal with navigation task.…”

GPU-based commonsense reasoning for real-time query answering and multimodal analysis

“…The approach aimed to add more unsolved nodes to the frontier set for efficient parallel execution. [66] implemented the idea to accelerate SSSP on GPUs. In the preprocessing step, the minimum weight of edges connected to a node u is calculated, ω(u) = min{w(u, v)|(u, v) ∈ E}.…”