Efficient Implementation of a Synchronous Parallel Push-Relabel Algorithm

TL;DR

This paper presents a highly efficient parallel implementation of the FIFO-based push-relabel algorithm for maximum flow problems, achieving significant speedups on large real-world graphs using coarse-grained parallelism.

Contribution

It introduces a novel parallel implementation that overcomes limitations of previous methods, demonstrating substantial performance improvements on modern multi-core systems.

Findings

Up to 12x speedup over sequential implementations

Up to 3x speedup over existing parallel methods

Effective on large real-world graph instances

Abstract

Motivated by the observation that FIFO-based push-relabel algorithms are able to outperform highest label-based variants on modern, large maximum flow problem instances, we introduce an efficient implementation of the algorithm that uses coarse-grained parallelism to avoid the problems of existing parallel approaches. We demonstrate good relative and absolute speedups of our algorithm on a set of large graph instances taken from real-world applications. On a modern 40-core machine, our parallel implementation outperforms existing sequential implementations by up to a factor of 12 and other parallel implementations by factors of up to 3.