Consider n nodes connected to a single coordinator. Each node receives an individual online data stream of numbers and, at any point in time, the coordinator has to know the k nodes currently observing the largest values, for a given k between 1 and n. We design and analyze an algorithm that solves this problem while bounding the amount of messages exchanged between the nodes and the coordinator. Our algorithm employs the idea of using filters which, intuitively speaking, leads to few messages to be sent, if the new input is "similar" to the previous ones. The algorithm uses a number of messages that is on expectation by a factor of O((log + k) log n) larger than that of an offline algorithm that sets filters in an optimal way, where is upper bounded by the largest value observed by any node.
A general approach to reduce the communication when monitoring distrib -uted data streams is proposed in @cite_3 . introduce the notion of , which are also an integral part of our algorithm presented in this paper. They consider a problem called continuous skyline maintenance, in which a coordinator is supposed to continuously maintain the skyline of dynamic objects. As they aim at minimizing the communication overhead between the coordinator and the objects, they use a filter method that helps in avoiding the transmission of updates from the objects to the coordinator in case these updates cannot influence the skyline maintained by the coordinator. More precisely, the dynamic objects are points of a @math -dimensional space and filters are hyper-rectangles assigned by the coordinator to the objects in such a way that as long as these points are within the assigned hyper-rectangle, updates need not be communicated to the coordinator.
@cite_3
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Existing work in the skyline literature focuses on optimizing the processing cost. This paper aims at minimization of the communication overhead in client-server architectures, where a server continuously maintains the skyline of dynamic objects. Our first contribution is a Filter method that avoids transmission of updates from objects that cannot influence the skyline. Specifically, each object is assigned a filter so that it needs to issue an update only if it violates its filter. Filter achieves significant savings over the naive approach of transmitting all updates. Going one step further, we introduce the concept of frequent skyline query over a sliding window(FSQW). The motivation is that snapshot skylines are not very useful in streaming environments because they keep changing over time. Instead, FSQW reports the objects that appear in the skylines of at least   s of the s most recent timestamps (0