论文标题
一种分布式算法，用于用于数据集群的应用程序的光谱稀疏
A Distributed Algorithm for Spectral Sparsification of Graphs with Applications to Data Clustering
论文作者
论文摘要
光谱稀疏性是一种用于减少正半芬太基基质中非零条目数量的技术，其光谱很小。特别是，光谱稀疏的主要应用是构造光谱接近给定密度图的稀疏图。我们研究了频谱的稀疏假设，即图表的边缘分配在可以相互交流的站点之间。在这项工作中，我们表明，如果将图分配在几个站点之间，则每个诱导子图的光谱稀疏器的结合为我们提供了原始图的光谱稀疏器。与文献中的其他作品相反，我们介绍了光谱稀疏器联合近似因子的精确计算，并对边缘重量进行了明确的计算。然后，当将输入数据作为派对站点之间的向日葵时，我们将此结果应用于多方通信复杂性的编号前面模型中的数据聚类。
Spectral sparsification is a technique that is used to reduce the number of non-zero entries in a positive semidefinite matrix with little changes to its spectrum. In particular, the main application of spectral sparsification is to construct sparse graphs whose spectra are close to a given dense graph. We study spectral sparsification under the assumption that the edges of a graph are allocated among sites which can communicate among each other. In this work we show that if a graph is allocated among several sites, the union of the spectral sparsifiers of each induced subgraph give us an spectral sparsifier of the original graph. In contrast to other works in the literature, we present precise computations of the approximation factor of the union of spectral sparsifiers and give an explicit calculation of the edge weights. Then we present an application of this result to data clustering in the Number-On-Forehead model of multiparty communication complexity when input data is allocated as a sunflower among sites in the party.
