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arXiv 2401.11580cs.ITmath.COmath.IT
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随机网络与二分网络中的Gossip年龄

Age of Gossip in Random and Bipartite Networks

Thomas Jacob Maranzatto

AI总结:

本文研究了gossip网络中的信息版本年龄(vAoI)指标,通过分析Erdős-Reyni随机图、随机d-正则图和二分网络,揭示了vAoI从线性到对数级的演变规律,并证明了相关阈值的存在性。

摘要:

本文研究gossip网络,其中一个观察过程的源节点向底层图发送更新。图中的节点通过随机发送更新与邻居通信。我们关注在各种网络类上研究信息版本年龄(vAoI)指标。已知$K_n$的版本年龄为对数级,而$\overline{K_n}$的版本年龄为线性。我们通过研究Erdős-Reyni随机图、随机$d$-正则图和二分网络,探讨“在$K_n$与$\overline{K_n}$之间插值时vAoI如何演变”的问题。主要结果是证明了在$G(n,p)$中存在一个从有理数级到对数级平均版本年龄的阈值,并证明对于常数$d$,$G(n,d)$几乎必然具有对数级版本年龄。我们还刻画了完全二分图$K_{L,R}$的版本年龄,其中$L$从$O(1)$变化到$O(n)$。

英文摘要:

In this paper we study gossip networks where a source observing a process sends updates to an underlying graph. Nodes in the graph communicate to their neighbors by randomly sending updates. Our interest is studying the version age of information (vAoI) metric over various classes of networks. It is known that the version age of $K_n$ is logarithmic, and the version age of $\overline{K_n}$ is linear. We study the question `how does the vAoI evolve as we interpolate between $K_n$ and $\overline{K_n}$' by studying Erdős-Reyni random graphs, random $d$-regular graphs, and bipartite networks. Our main results are proving the existence of a threshold in $G(n,p)$ from rational to logarithmic average version age, and showing $G(n,d)$ almost surely has logarithmic version age for constant $d$. We also characterize the version age of complete bipartite graphs $K_{L,R}$, when we let $L$ vary from $O(1)$ to $O(n)$.

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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