文章基本信息

标题：Average Whenever You Meet: Opportunistic Protocols for Community Detection
本地全文：下载
作者：Luca Becchetti ; Andrea Clementi ; Pasin Manurangsi 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2018
卷号：112
页码：1-13
DOI：10.4230/LIPIcs.ESA.2018.7
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Consider the following asynchronous, opportunistic communication model over a graph G: in each round, one edge is activated uniformly and independently at random and (only) its two endpoints can exchange messages and perform local computations. Under this model, we study the following random process: The first time a vertex is an endpoint of an active edge, it chooses a random number, say +/- 1 with probability 1/2; then, in each round, the two endpoints of the currently active edge update their values to their average. We provide a rigorous analysis of the above process showing that, if G exhibits a two-community structure (for example, two expanders connected by a sparse cut), the values held by the nodes will collectively reflect the underlying community structure over a suitable phase of the above process. Our analysis requires new concentration bounds on the product of certain random matrices that are technically challenging and possibly of independent interest. We then exploit our analysis to design the first opportunistic protocols that approximately recover community structure using only logarithmic (or polylogarithmic, depending on the sparsity of the cut) work per node.
关键词：Community Detection; Random Processes; Spectral Analysis