Alternative set-theoretical algorithms for efficient computations of cliques in Vietoris-Rips complexes

TL;DR

This paper introduces novel set-theoretical algorithms for efficiently computing cliques in Vietoris-Rips complexes, addressing computational bottlenecks and outperforming existing Python solutions in large-scale network analysis.

Contribution

It presents new set-theoretical algorithms specifically designed for clique computation, improving performance over classic methods and existing implementations.

Findings

Proposed algorithms outperform existing Python-based solutions.

Set-theoretical approaches reduce computational time and memory usage.

Benchmark results demonstrate significant performance gains.

Abstract

Identifying cliques in dense networks remains a formidable challenge, even with significant advances in computational power and methodologies. To tackle this, numerous algorithms have been developed to optimize time and memory usage, implemented across diverse programming languages. Yet, the inherent NP-completeness of the problem continues to hinder performance on large-scale networks, often resulting in memory leaks and slow computations. In the present study, we critically evaluate classic algorithms to pinpoint computational bottlenecks and introduce novel set-theoretical approaches tailored for network clique computation. Our proposed algorithms are rigorously implemented and benchmarked against existing Python-based solutions, demonstrating superior performance. These findings underscore the potential of set-theoretical techniques to drive substantial performance gains in network analysis.