标题： 用于维托里斯-里普斯复形中团高效计算的替代集合论算法 显示英文标题

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

摘要： 在密集网络中识别团仍然是一个艰巨的挑战，即使计算能力和方法有了显著进步。 为了解决这个问题，已经开发了许多算法来优化时间和内存使用，并在多种编程语言中实现。 然而，该问题固有的NP完全性继续阻碍大规模网络的性能，通常导致内存泄漏和计算缓慢。 在本研究中，我们对经典算法进行了批判性评估，以确定计算瓶颈，并引入了针对网络团计算的新型集合论方法。 我们提出的算法被严格实现并与现有的基于Python的解决方案进行了基准测试，表现出优越的性能。 这些发现强调了集合论技术在推动网络分析中显著性能提升方面的潜力。 显示英文摘要

摘要： 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.