加权时序网络中的快速极大团枚举
Fast maximal clique enumeration in weighted temporal networks
AI总结：
本文提出高效的加权时序网络 (delta,gamma)-极大团枚举算法，改进两阶段流程并实现线性初始阶段与搜索剪枝，在真实数据集上较现有方法取得数个数量级加速。
摘要：
团是网络中完全连接的节点组，通常用于研究复杂系统的群体动态。在现实场景中，群体动态往往具有时间成分，例如会议参会者从一个群体对话转移到另一个群体对话。近来，已有研究引入极大团枚举方法，通过加入时间（以及频率）约束来解释此类现象，这些方法会枚举所谓的 (delta,gamma)-极大团。在本工作中，我们提出一种高效的 (delta,gamma)-极大团枚举算法，将 gamma 从频率约束扩展为更通用的加权约束。此外，我们给出一种 (delta,gamma)-团的定义，解决了时序领域现有定义存在的一个问题。我们的方法受到当前最优两阶段方法的启发，引入了更高效的初始（拉伸）阶段。具体而言，我们将该阶段的时间复杂度降低为相对于时序边数呈线性。进一步地，我们为第二（归并）阶段引入一种新方法，使我们能够高效剪枝搜索树分支。因此，在多个（大型）真实数据集上的实验中，我们观察到通常可达数个数量级的加速。我们的算法在时序网络上大幅优于现有最优方法，同时将适用性扩展到加权网络。
英文摘要：
Cliques, groups of fully connected nodes in a network, are often used to study group dynamics of complex systems. In real-world settings, group dynamics often have a temporal component. For example, conference attendees moving from one group conversation to another. Recently, maximal clique enumeration methods have been introduced that add temporal (and frequency) constraints, to account for such phenomena. These methods enumerate so called (delta,gamma)-maximal cliques. In this work, we introduce an efficient (delta,gamma)-maximal clique enumeration algorithm, that extends gamma from a frequency constraint to a more versatile weighting constraint. Additionally, we introduce a definition of (delta,gamma)-cliques, that resolves a problem of existing definitions in the temporal domain. Our approach, which was inspired by a state-of-the-art two-phase approach, introduces a more efficient initial (stretching) phase. Specifically, we reduce the time complexity of this phase to be linear with respect to the number of temporal edges. Furthermore, we introduce a new approach to the second (bulking) phase, which allows us to efficiently prune search tree branches. Consequently, in experiments we observe speed-ups, often by several order of magnitude, on various (large) real-world datasets. Our algorithm vastly outperforms the existing state-of-the-art methods for temporal networks, while also extending applicability to weighted networks.
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