一种适用于稀疏图和重尾稀疏图的通用无损压缩方法

Payam Delgosha, V. Anantharam
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引用次数: 2

摘要

图形数据在一些现代应用中自然出现,包括但不限于互联网图表、社交网络、基因组学和蛋白质组学。典型的大型图形数据说明了为此类数据设计通用压缩方法的重要性。在大多数应用程序中,图形数据是稀疏的,这意味着图形中边的数量比$n^{2}$的扩展速度要慢,其中$n$表示顶点的数量。虽然在某些应用中,边的数量随$n$线性扩展,但在其他应用中,边的数量远小于$n^{2}$,但似乎随$n$超线性扩展。我们称前者为稀疏图,后者为重尾稀疏图。本文介绍了一种同时适用于这两类数据的通用无损压缩方法。我们采用稀疏图的局部弱收敛框架和重尾稀疏图的稀疏图框架来实现这一点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Universal Lossless Compression Method applicable to Sparse Graphs and heavy-tailed Sparse Graphs
Graphical data arises naturally in several modern applications, including but not limited to internet graphs, social networks, genomics and proteomics. The typically large size of graphical data argues for the importance of designing universal compression methods for such data. In most applications, the graphical data is sparse, meaning that the number of edges in the graph scales more slowly than $n^{2}$, where $n$ denotes the number of vertices. Although in some applications the number of edges scales linearly with $n$, in others the number of edges is much smaller than $n^{2}$ but appears to scale superlinearly with $n$. We call the former sparse graphs and the latter heavy-tailed sparse graphs. In this paper we introduce a universal lossless compression method which is simultaneously applicable to both classes. We do this by employing the local weak convergence framework for sparse graphs and the sparse graphon framework for heavy-tailed sparse graphs.
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