森林贴近度中心性的新近似算法--对单个顶点和顶点组的逼近
New Approximation Algorithms for Forest Closeness Centrality -- for Individual Vertices and Vertex Groups
摘要：
海量图数据集的出现需要快速的挖掘算法。在图挖掘中，识别重要顶点的中心性度量是最流行的分析方法。一个越来越受到关注的措施是森林接近中心性;它与使用电流的电气措施密切相关，但也可以处理断开的图形。最近，[Jin等人，ICDM'19]提出了一种算法来近似这个措施的概率。他们的算法可以快速处理小的输入，但不能扩展到超过数十万个顶点。在本文中，我们首先提出了一个不同的近似算法，它是两个数量级的速度和更准确的实践。我们的方法利用强连接的统一生成树和森林的距离适应和扩展最近的近似算法相关的单顶点问题。这导致了具有绝对概率误差保证的近线性时间算法。此外，我们是第一个考虑的问题，找到一个最佳组的顶点w.r.t.森林封闭我们证明后一个问题是NP难的;为了近似它，我们采用了一种贪心算法[Li et al.，WWW'19]，其基于（部分）矩阵求逆。此外，我们的实验表明，在不连通图，组森林的封闭性优于现有的中心性措施的上下文中的半监督顶点分类。
英文摘要：
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest closeness centrality; it is closely related to electrical measures using current flow but can also handle disconnected graphs. Recently, [Jin et al., ICDM'19] proposed an algorithm to approximate this measure probabilistically. Their algorithm processes small inputs quickly, but does not scale well beyond hundreds of thousands of vertices. In this paper, we first propose a different approximation algorithm; it is up to two orders of magnitude faster and more accurate in practice. Our method exploits the strong connection between uniform spanning trees and forest distances by adapting and extending recent approximation algorithms for related single-vertex problems. This results in a nearly-linear time algorithm with an absolute probabilistic error guarantee. In addition, we are the first to consider the problem of finding an optimal group of vertices w.r.t. forest closeness. We prove that this latter problem is NP-hard; to approximate it, we adapt a greedy algorithm by [Li et al., WWW'19], which is based on (partial) matrix inversion. Moreover, our experiments show that on disconnected graphs, group forest closeness outperforms existing centrality measures in the context of semi-supervised vertex classification.
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