Fast Parallel Algorithms for Enumeration of Simple, Temporal, and Hop-Constrained Cycles

TL;DR

This paper develops scalable fine-grained parallel algorithms for enumerating simple, temporal, and hop-constrained cycles in graphs, significantly improving speed and scalability over coarse-grained methods.

Contribution

It introduces a novel fine-grained parallelization approach for cycle enumeration algorithms, demonstrating near-linear scalability and substantial speedups on multi-core clusters.

Findings

Fine-grained parallel algorithms are strongly scalable.

Achieved near-linear scalability on 256 CPU cores.

Obtained an order of magnitude speedup over coarse-grained methods.

Abstract

Cycles are one of the fundamental subgraph patterns and being able to enumerate them in graphs enables important applications in a wide variety of fields, including finance, biology, chemistry, and network science. However, to enable cycle enumeration in real-world applications, efficient parallel algorithms are required. In this work, we propose scalable parallelisation of state-of-the-art sequential algorithms for enumerating simple, temporal, and hop-constrained cycles. First, we focus on the simple cycle enumeration problem and parallelise the algorithms by Johnson and by Read and Tarjan in a fine-grained manner. We theoretically show that our resulting fine-grained parallel algorithms are scalable, with the fine-grained parallel Read-Tarjan algorithm being strongly scalable. In contrast, we show that straightforward coarse-grained parallel versions of these simple cycle enumeration algorithms that exploit edge- or vertex-level parallelism are not scalable. Next, we adapt our fine-grained approach to enable the enumeration of cycles under time-window, temporal, and hop constraints. Our evaluation on a cluster with 256 CPU cores that can execute up to 1024 simultaneous threads demonstrates a near-linear scalability of our fine-grained parallel algorithms when enumerating cycles under the aforementioned constraints. On the same cluster, our fine-grained parallel algorithms achieve, on average, one order of magnitude speedup compared to the respective coarse-grained parallel versions of the state-of-the-art algorithms for cycle enumeration. The performance gap between the fine-grained and the coarse-grained parallel algorithms increases as we use more CPU cores.