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Issue No.02  February (2010 vol.22)
pp: 193206
KenHao Liu , National Taiwan University, Taipei
WeiGuang Teng , National Cheng Kung University, Taipei
MingSyan Chen , National Taiwan University, Taipei
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TKDE.2009.51
ABSTRACT
Due to the dynamic nature of data streams, a sliding window is used to generate synopses that approximate the most recent data within the retrospective horizon to answer queries or discover patterns. In this paper, we propose a dynamic scheme for wavelet synopses management in sensor networks. We define a data structure Sliding Dual Tree, abbreviated as SDT, to generate dynamic synopses that adapts to the insertions and deletions in the most recent sliding window. By exploiting the properties of Haar wavelet transform, we develop several operations to incrementally maintain SDT over consecutive time windows in a time and spaceefficient manner. These operations directly operate on the transformed timefrequency domain without the need of storing/reconstructing the original data. As shown in our thorough analysis, our SDTbased approach greatly reduces the required resources for synopses generation and maximizes the storage utilization of wavelet synopses in terms of the window length and quality measures. We also show that the approximation error of the dynamic wavelet synopses, i.e., L^{2}norm error, can be incrementally updated. We also derive the bound of the overestimation of the approximation error due to the incremental thresholding scheme. Furthermore, the synopses can be used to answer various kinds of numerical queries such as point and distance queries. In addition, we show that our SDT can adapt to resource allocation to further enhance the overall storage utilization over time. As demonstrated by our experimental results, our proposed framework can outperform current techniques in both real and synthetic data.
INDEX TERMS
Data stream, wavelet transform, dynamic synopses.
CITATION
KenHao Liu, WeiGuang Teng, MingSyan Chen, "Dynamic Wavelet Synopses Management over Sliding Windows in Sensor Networks", IEEE Transactions on Knowledge & Data Engineering, vol.22, no. 2, pp. 193206, February 2010, doi:10.1109/TKDE.2009.51
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