The Floyd-Warshall Algorithm Re-implemented Using 3D-Tensors and Hardware Acceleration

TL;DR

This paper presents a GPU-accelerated implementation of the Floyd-Warshall algorithm and R-Kleene for solving the all-pairs shortest path problem, demonstrating significant speedups over traditional CPU-based methods.

Contribution

It introduces a novel GPU-based implementation of Floyd-Warshall using PyTorch, along with a recursive R-Kleene algorithm and a flexible graph generator for performance evaluation.

Findings

GPU implementations outperform NetworkX in runtime

R-Kleene shows competitive performance on large graphs

Open-source code facilitates further research and benchmarking

Abstract

The Floyd-Warshall(FW) algorithm, is an ancient but a largely important algorithm used to solve the all-pairs simple-paths(APSP) problem. While the algorithm is available for use in open-source graph optimization libraries such as NetworkX, they do not take advantage of modern parallel processing hardware such as Graphics Processing Units(GPUs), which would reduce compute time to a fraction of its iterative or recursive implementations. In this work, a re-implementation of the Floyd-Warshall algorithm using open-source GPU libraries such as PyTorch is presented. A further implementation of the R-Kleene is also described, a slightly newer algorithm used for solving the APSP problem in a divide-and-conquer, recursive but highly parallelized architecture. In addition, a random graph generator that generates a wide range of graphs of different scales is also contributed, where the densities and connectivities are controlled using some heuristics. The run-times of the GPU accelerated FW algorithm and R-Kleene on these heuristically generated graphs are evaluated against each other and to the widely used implementation from NetworkX. The code for the GPU implementation of the algorithms, the random graph generator, and the Blender animation file are available at https://github.com/tanjary21/APSP_GPU/.