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
1987187649 2109821166 1604641903 2200550062
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 θ ⋅ s of the s most recent timestamps (0 The skyline of a multidimensional data set contains the "best" tuples according to any preference function that is monotonic on each dimension. Although skyline computation has received considerable attention in conventional databases, the existing algorithms are inapplicable to stream applications because 1) they assume static data that are stored in the disk (rather than continuously arriving expiring), 2) they focus on "one-time" execution that returns a single skyline (in contrast to constantly tracking skyline changes), and 3) they aim at reducing the I O overhead (as opposed to minimizing the CPU-cost and main-memory consumption). This paper studies skyline computation in stream environments, where query processing takes into account only a "sliding window" covering the most recent tuples. We propose algorithms that continuously monitor the incoming data and maintain the skyline incrementally. Our techniques utilize several interesting properties of stream skylines to improve space time efficiency by expunging data from the system as early as possible (i.e., before their expiration). Furthermore, we analyze the asymptotical performance of the proposed solutions, and evaluate their efficiency with extensive experiments. We consider the online problem for a root (or a coordinator) to maintain a set of filters for the purpose of keeping track of the dominance relationship of some distributed multi-dimensional data. Such data keep changing from time to time. The objective is to minimize the communication between the root and the distributed data sources. Assume that data are chosen from the d-dimensional grid 1, 2, ..., U d, we give an O(d log U)-competitive algorithm for this online problem. The competitive ratio is asymptotically tight as it is relatively easy to show an Ω(d log U) lower bound. There has been an increased growth in a number of applications that naturally generate large volumes of uncertain data. By the advent of such applications, the support of advanced analysis queries such as the skyline and its variant operators for big uncertain data has become important. In this paper, we propose the effective parallel algorithms using MapReduce to process the probabilistic skyline queries for uncertain data modeled by both discrete and continuous models. We present three filtering methods to identify probabilistic non-skyline objects in advance. We next develop a single MapReduce phase algorithm PS-QP-MR by utilizing space partitioning based on a variant of quadtrees to distribute the instances of objects effectively and the enhanced algorithm PS-QPF-MR by applying the three filtering methods additionally. We also propose the workload balancing technique to balance the workload of reduce functions based on the number of machines available. Finally, we present the brute-force algorithms PS-BR-MR and PS-BRF-MR with partitioning randomly and applying the filtering methods. In our experiments, we demonstrate the efficiency and scalability of PS-QPF-MR compared to the other algorithms.