分布式流Top-k-Position监控近似的竞争算法研究
On Competitive Algorithms for Approximations of Top-k-Position Monitoring of Distributed Streams
摘要：
考虑连续分布式监视模型，其中接收单个数据流的$n$分布式节点连接到指定的服务器。服务器被要求持续监视在所有流上观察到的值上定义的函数，同时最小化通信。我们研究了一种变体，其中服务器配备有广播信道，并且应该跟踪当前观察$k$最大值的节点集合的近似值。这样的近似集是精确的，除了在$k$第一个最大值的$\varepsilon$邻域中存在一些不精确之外。在观测值的边际变化（例如，由于噪声）可以被忽略的情况下，顶部- $k$ -位置监测问题的这种近似是令人感兴趣的，使得监测近似是足够的并且可以减少通信。本文扩展了[IPDPS'15]的结果，在那里我们开发了一个基于过滤器的在线算法（精确）Top-k-Position监控问题。在那里，我们提出了一个竞争力分析我们的算法对离线对手，也仅限于基于过滤器的算法。我们的新算法及其分析使用新方法。我们分析了它们对使用精确和近似基于过滤器的算法的对手的竞争力，并观察到这些对手的各自权力之间的严重差异。
英文摘要：
Consider the continuous distributed monitoring model in which $n$ distributed nodes, receiving individual data streams, are connected to a designated server. The server is asked to continuously monitor a function defined over the values observed across all streams while minimizing the communication. We study a variant in which the server is equipped with a broadcast channel and is supposed to keep track of an approximation of the set of nodes currently observing the $k$ largest values. Such an approximate set is exact except for some imprecision in an $\varepsilon$-neighborhood of the $k$-th largest value. This approximation of the Top-$k$-Position Monitoring Problem is of interest in cases where marginal changes (e.g. due to noise) in observed values can be ignored so that monitoring an approximation is sufficient and can reduce communication. This paper extends our results from [IPDPS'15], where we have developed a filter-based online algorithm for the (exact) Top-k-Position Monitoring Problem. There we have presented a competitive analysis of our algorithm against an offline adversary that also is restricted to filter-based algorithms. Our new algorithms as well as their analyses use new methods. We analyze their competitiveness against adversaries that use both exact and approximate filter-based algorithms, and observe severe differences between the respective powers of these adversaries.
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。
