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arXiv 2305.09705cs.LGcs.ITmath.IT
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随机边编码:大型标记图的一次性回退比特编码

Random Edge Coding: One-Shot Bits-Back Coding of Large Labeled Graphs

University of Toronto(多伦多大学);Vector Institute for Artificial Inteligence(向量人工智能研究所);University of Amsterdam(阿姆斯特丹大学)

Daniel Severo, James Townsend, Ashish Khisti, Alireza Makhzani

AI总结:

本文提出了一种名为Random Edge Coding的大型标记图一次性压缩方法,结合Pólya's Urn无参数模型实现准线性计算和线性内存复杂度,利用回退比特编码保留图结构,并在真实数据集上展现出竞争力的压缩性能和良好扩展性。

摘要:

我们提出了一种用于压缩大型标记图的一次性方法,称为Random Edge Coding。当与基于Pólya's Urn的无参数模型结合使用时,最坏情况下的计算和内存复杂度随观察到的边数呈准线性和线性扩展,使其在稀疏图上非常高效,且仅需整数运算。我们方法的关键是回退比特编码,它用于从边列表中无放回地采样边和顶点,从而保留图的结构。在边排列和边内顶点排列保持不变的一类随机图模型下证明了最优性。实验表明,Random Edge Coding在真实网络数据集上能实现具有竞争力的压缩性能,并可扩展到具有数百万节点和边的图。

英文摘要:

We present a one-shot method for compressing large labeled graphs called Random Edge Coding. When paired with a parameter-free model based on Pólya's Urn, the worst-case computational and memory complexities scale quasi-linearly and linearly with the number of observed edges, making it efficient on sparse graphs, and requires only integer arithmetic. Key to our method is bits-back coding, which is used to sample edges and vertices without replacement from the edge-list in a way that preserves the structure of the graph. Optimality is proven under a class of random graph models that are invariant to permutations of the edges and of vertices within an edge. Experiments indicate Random Edge Coding can achieve competitive compression performance on real-world network datasets and scales to graphs with millions of nodes and edges.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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