Approximating Betweenness Centrality in Fully Dynamic Networks

Q3 Mathematics
E. Bergamini, Henning Meyerhenke
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引用次数: 35

Abstract

Abstract Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Because exact computations are prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in networks that change over time. In this article, we propose the first betweenness centrality approximation algorithms with a provable guarantee on the maximum approximation error for dynamic networks. Several new intermediate algorithmic results contribute to the respective approximation algorithms: (i) new upper bounds on the vertex diameter, (ii) the first fully dynamic algorithm for updating an approximation of the vertex diameter in undirected graphs, and (iii) an algorithm with lower time complexity for updating single-source shortest paths in unweighted graphs after a batch of edge actions. Using approximation, our algorithms are the first to make in-memory computation of betweenness in dynamic networks with millions of edges feasible. Our experiments show that our algorithms can achieve substantial speedups compared to recomputation, up to several orders of magnitude. Moreover, the approximation accuracy is usually significantly better than the theoretical guarantee in terms of absolute error. More importantly, for reasonably small approximation error thresholds, the rank of nodes is well preserved, in particular for nodes with high betweenness.
全动态网络的中间中心性逼近
中间度是一种众所周知的中心性度量,它根据节点在最短路径中的参与度对网络节点进行排序。由于在大型网络中难以进行精确计算,因此提出了几种近似算法。除此之外,近年来出现了动态算法的发表,这些算法用于在随时间变化的网络中有效地重新计算中间性。在本文中,我们提出了对动态网络的最大逼近误差有可证明保证的第一类中间性中心性逼近算法。几个新的中间算法结果有助于各自的近似算法:(i)顶点直径的新上界,(ii)在无向图中更新顶点直径近似的第一个完全动态算法,以及(iii)在一批边缘动作后更新无加权图中单源最短路径的时间复杂度较低的算法。使用近似,我们的算法是第一个在具有数百万条边的动态网络中实现内存计算的算法。我们的实验表明,与重新计算相比,我们的算法可以实现显著的加速,高达几个数量级。而且,在绝对误差方面,近似精度通常明显优于理论保证。更重要的是,对于相当小的近似误差阈值,节点的秩被很好地保留,特别是对于具有高中间度的节点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Internet Mathematics
Internet Mathematics Mathematics-Applied Mathematics
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