• 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.