A GPU-based parallel algorithm for enumerating all chordless cycles in graphs

TL;DR

This paper introduces a GPU-based parallel algorithm implemented in OpenCL for efficiently enumerating all chordless cycles in graphs, significantly improving performance on graphs with many such cycles compared to previous sequential methods.

Contribution

It presents a novel GPU parallel algorithm with a compact data structure for enumerating chordless cycles, outperforming sequential algorithms on large graphs.

Findings

Significant speedup on graphs with many chordless cycles

Efficient memory usage suitable for GPU constraints

Outperforms previous sequential algorithms in execution time

Abstract

In a finite undirected simple graph, a chordless cycle is an induced subgraph which is a cycle. We propose a GPU parallel algorithm for enumerating all chordless cycles of such a graph. The algorithm, implemented in OpenCL, is based on a previous sequential algorithm developed by the current authors for the same problem. It uses a more compact data structure for solution representation which is suitable for the memory-size limitation of a GPU. Moreover, for graphs with a sufficiently large amount of chordless cycles, the algorithm presents a significant improvement in execution time that outperforms the sequential method.