有界入度下的谣言传播
Rumor Spreading with Bounded In-Degree
摘要：
在用于在网络中传播信息的经典的基于流言的通信模型中，在每个时间单元中，允许每个节点$u$联系单个随机邻居$v$。如果$u$知道要传播的数据（谣言），则它将其传播到$v$（称为PUSH），如果不知道，则它向$v$（称为PUSH）请求该数据。在经典的流言模型中，每个节点在每个时间单位内只允许联系一个邻居，而每个节点可能被许多邻居节点联系。在本文中，我们考虑一个限制模型，在每个节点只有一个传入的请求可以服务。只要只需要传播一条信息，这对推送请求没有影响。然而，它对pull request有很大的影响。因此，在本文中，我们集中在这个较弱的拉动版本，我们称之为“限制拉”。我们区分两个版本的限制拉协议取决于是否在一组拉请求在一个给定的节点中被服务的请求是随机选择adversarally或均匀。作为第一个结果，我们证明了两个变量之间的指数分离。我们表明，有这样的情况下，如果对手挑选的请求提供服务，限制拉协议需要一个多项式数量的轮，而如果获胜的请求是随机选择均匀，限制拉协议只需要一个polylogarithmic数量的轮通知整个网络。此外，作为主要的技术贡献，我们表明，如果要提供服务的请求是随机选择的，使用限制拉与使用经典的拉协议的速度可以w.h.p.上界由$O(Δ/ δ\log n)$，其中$Δ$和$δ$是最大和最小的网络度。
英文摘要：
In the classic gossip-based model of communication for disseminating information in a network, in each time unit, every node $u$ is allowed to contact a single random neighbor $v$. If $u$ knows the data (rumor) to be disseminated, it disperses it to $v$ (known as PUSH) and if it does not, it requests it from $v$ (known as PULL). While in the classic gossip model, each node is only allowed to contact a single neighbor in each time unit, each node can possibly be contacted by many neighboring nodes. In the present paper, we consider a restricted model where at each node only one incoming request can be served. As long as only a single piece of information needs to be disseminated, this does not make a difference for push requests. It however has a significant effect on pull requests. In the paper, we therefore concentrate on this weaker pull version, which we call 'restricted pull'. We distinguish two versions of the restricted pull protocol depending on whether the request to be served among a set of pull requests at a given node is chosen adversarially or uniformly at random. As a first result, we prove an exponential separation between the two variants. We show that there are instances where if an adversary picks the request to be served, the restricted pull protocol requires a polynomial number of rounds whereas if the winning request is chosen uniformly at random, the restricted pull protocol only requires a polylogarithmic number of rounds to inform the whole network. Further, as the main technical contribution, we show that if the request to be served is chosen randomly, the slowdown of using restricted pull versus using the classic pull protocol can w.h.p. be upper bounded by $O(Δ/ δ\log n)$, where $Δ$ and $δ$ are the largest and smallest degree of the network.
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。
