arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1202.2092cs.DCcs.DMcs.DS
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通过八卦发现

Discovery through Gossip

Bernhard Haeupler, Gopal Pandurangan, David Peleg, Rajmohan Rajaraman, Zhifeng Sun

摘要:

我们研究了动态网络中基于随机流言的过程,这些过程的动机是大规模分布式网络(如对等网络或社交网络)中的发现过程。对等网络中的一个研究得很好的问题是资源发现问题。在那里,节点(具有IP地址的主机)的目标是发现所有其他主机的IP地址。在社交网络中,节点(人)通过与邻居(朋友)交换联系人来发现新的节点。在这两种情况下,新节点的发现都会改变底层网络-新的边被添加到网络中-并且该过程在改变的网络中继续。严格分析这种动态(随机)过程与连续的自我变化的拓扑结构仍然是一个具有挑战性的问题,具有明显的应用。本文研究和分析了两种基于流言的自然发现过程。在推送过程中,每个节点重复地选择两个随机邻居并使它们接触(即,将它们的互信息“推”给彼此)。在拉发现过程中,每个节点重复地从随机邻居请求或“拉”随机联系。这两个过程都是轻量级的,本地的,并且由于它们的随机性而自然健壮。我们的主要结果是这两个随机过程收敛所需的时间几乎紧的分析。我们证明了在任何无向n节点图中,这两个过程都需要O(n log^2 n)轮以高概率将每个节点连接到所有其他节点,而Omega(n log n)是一个下界。在有向情况下,我们给出了强连通有向图的O(n^2 log n)上界和Omega(n^2)下界。我们克服的一个关键技术挑战是分析一个随机过程,这个过程本身会导致一个不断变化的网络,从而导致每一轮都有复杂的依赖关系。

英文摘要:

We study randomized gossip-based processes in dynamic networks that are motivated by discovery processes in large-scale distributed networks like peer-to-peer or social networks. A well-studied problem in peer-to-peer networks is the resource discovery problem. There, the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying network - new edges are added to the network - and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes with a continuously self-changing topology remains a challenging problem with obvious applications. This paper studies and analyzes two natural gossip-based discovery processes. In the push process, each node repeatedly chooses two random neighbors and puts them in contact (i.e., "pushes" their mutual information to each other). In the pull discovery process, each node repeatedly requests or "pulls" a random contact from a random neighbor. Both processes are lightweight, local, and naturally robust due to their randomization. Our main result is an almost-tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n-node graph both processes take O(n log^2 n) rounds to connect every node to all other nodes with high probability, whereas Omega(n log n) is a lower bound. In the directed case we give an O(n^2 log n) upper bound and an Omega(n^2) lower bound for strongly connected directed graphs. A key technical challenge that we overcome is the analysis of a randomized process that itself results in a constantly changing network which leads to complicated dependencies in every round.

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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