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On Query Processing and Optimality Using Spectral Locality-Preserving Mappings

  • Mohamed F. Mokbel
  • Walid G. Aref
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2750)

Abstract

A locality-preserving mapping (LPM) from the multi-dimensional space into the one-dimensional space is beneficial for many applications (e.g., range queries, nearest-neighbor queries, clustering, and declustering) when multi-dimensional data is placed into one-dimensional storage (e.g., the disk). The idea behind a locality-preserving mapping is to map points that are nearby in the multi-dimensional space into points that are nearby in the one-dimensional space. For the past two decades, fractals (e.g., the Hilbert and Peano space-filling curves) have been considered the natural method for providing a locality-preserving mapping to support efficient answer for range queries and similarity search queries. In this paper, we go beyond the idea of fractals. Instead, we investigate a locality-preserving mapping algorithm (The Spectral LPM) that uses the spectrum of the multi-dimensional space. This paper provably demonstrates how Spectral LPM provides a globally optimal mapping from the multi-dimensional space to the one-dimensional space, and hence outperforms fractals. As an application, in the context of range queries and nearest-neighbor queries, empirical results of the performance of Spectral LPM validate our analysis in comparison with Peano, Hilbert, and Gray fractal mappings.

Keywords

Query Processing Linear Span Range Query Laplacian Matrix Manhattan Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Mohamed F. Mokbel
    • 1
  • Walid G. Aref
    • 1
  1. 1.Department of Computer SciencesPurdue University 

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