• Journal of KIISE:Databases
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• v.33 no.7
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• pp.693-707
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• 2006

To improve performance using a multidimensional index in similar sequence matching, we transform a high-dimensional sequence to a low-dimensional sequence, and then construct a low-dimensional MBR that contains multiple transformed sequences. In this paper we propose a formal method that transforms a high-dimensional MBR itself to a low-dimensional MBR, and show that this method significantly reduces the number of lower-dimensional transformations. To achieve this goal, we first formally define the new notion of MBR-safe. We say that a transform is MBR-safe if a low-dimensional MBR to which a high-dimensional MBR is transformed by the transform contains every individual low-dimensional sequence to which a high-dimensional sequence is transformed. We then propose two MBR-safe transforms based on DFT and DCT, the most representative lower-dimensional transformations. For this, we prove the traditional DFT and DCT are not MBR-safe, and define new transforms, called mbrDFT and mbrDCT, by extending DFT and DCT, respectively. We also formally prove these mbrDFT and mbrDCT are MBR-safe. Moreover, we show that mbrDFT(or mbrDCT) is optimal among the DFT-based(or DCT-based) MBR-safe transforms that directly convert a high-dimensional MBR itself into a low-dimensional MBR. Analytical and experimental results show that the proposed mbrDFT and mbrDCT reduce the number of lower-dimensional transformations drastically, and improve performance significantly compared with the $na\"{\i}ve$ transforms. These results indicate that our MBR- safe transforms provides a useful framework for a variety of applications that require the lower-dimensional transformation of high-dimensional MBRs.

• Journal of KIISE:Databases
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• v.34 no.6
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• pp.503-517
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• 2007

In this paper we address the MBR-safe property of Piecewise Aggregation Approximation(PAA), and propose an of efficient subsequence matching method based on the MBR-safe PAA. A transformation is said to be MBR-safe if a low-dimensional MBR to which a high- dimensional MBR is transformed by the transformation contains every individual low-dimensional sequence to which a high-dimensional sequence is transformed. Using an MBR-safe transformation we can reduce the number of lower-dimensional transformations required in similar sequence matching, since it transforms a high-dimensional MBR itself to a low-dimensional MBR directly. Furthermore, PAA is known as an excellent lower-dimensional transformation single its computation is very simple, and its performance is superior to other transformations. Thus, to integrate these advantages of PAA and MBR-safeness, we first formally confirm the MBR-safe property of PAA, and then improve subsequence matching performance using the MBR-safe PAA. Contributions of the paper can be summarized as follows. First, we propose a PAA-based MBR-safe transformation, called mbrPAA, and formally prove the MBR-safeness of mbrPAA. Second, we propose an mbrPAA-based subsequence matching method, and formally prove its correctness of the proposed method. Third, we present the notion of entry reuse property, and by using the property, we propose an efficient method of constructing high-dimensional MBRs in subsequence matching. Fourth, we show the superiority of mbrPAA through extensive experiments. Experimental results show that, compared with the previous approach, our mbrPAA is 24.2 times faster in the low-dimensional MBR construction and improves subsequence matching performance by up to 65.9%.