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The Pyramid-Technique: Towards Breaking the Curse of Dimensionality.

Stefan Berchtold, Christian Böhm, Hans-Peter Kriegel: The Pyramid-Technique: Towards Breaking the Curse of Dimensionality. SIGMOD Conference 1998: 142-153
@inproceedings{DBLP:conf/sigmod/BerchtoldBK98,
  author    = {Stefan Berchtold and
               Christian B{\"o}hm and
               Hans-Peter Kriegel},
  editor    = {Laura M. Haas and
               Ashutosh Tiwary},
  title     = {The Pyramid-Technique: Towards Breaking the Curse of Dimensionality},
  booktitle = {SIGMOD 1998, Proceedings ACM SIGMOD International Conference
               on Management of Data, June 2-4, 1998, Seattle, Washington, USA},
  publisher = {ACM Press},
  year      = {1998},
  isbn      = {0-89791-995-5},
  pages     = {142-153},
  ee        = {http://doi.acm.org/10.1145/276304.276318},
  crossref  = {DBLP:conf/sigmod/98},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

Abstract

In this paper, we propose the Pyramid-Technique, a new indexing method for high-dimensional data spaces. The Pyramid-Technique is highly adapted to range query processing using the maximum metric Lmax. In contrast to all other index structures, the performance of the Pyramid-Technique does not deteriorate when processing range queries on data of higher dimensionality. The Pyramid-Technique is based on a special partitioning strategy which is optimized for high-dimensional data. The basic idea is to divide the data space first into 2d pyramids sharing the center point of the space as a top. In a second step, the single pyramids are cut into slices parallel to the basis of the pyramid. These slices form the data pages. Furthermore, we show that this partition provides a mapping from the given d-dimensional space to a 1-dimensional space. Therefore, we are able to use a B+-tree to manage the transformed data. As an analytical evaluation of our technique for hypercube range queries and uniform data distribution shows, the Pyramid-Technique clearly outperforms index structures using other partitioning strategies. To demonstrate the practical relevance of our technique, we experimentally compared the Pyramid-Technique with the X-tree, the Hilbert R-tree, and the Linear Scan. The results of our experiments using both, synthetic and real data, demonstrate that the Pyramid-Technique outperforms the X-tree and the Hilbert R-tree by a factor of up to 14 (number of page accesses) and up to 2500 (total elapsed time) for range queries.

Copyright © 1998 by the ACM, Inc., used by permission. Permission to make digital or hard copies is granted provided that copies are not made or distributed for profit or direct commercial advantage, and that copies show this notice on the first page or initial screen of a display along with the full citation.


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Laura M. Haas, Ashutosh Tiwary (Eds.): SIGMOD 1998, Proceedings ACM SIGMOD International Conference on Management of Data, June 2-4, 1998, Seattle, Washington, USA. ACM Press 1998, ISBN 0-89791-995-5 CiteSeerX Google scholar pubzone.org BibTeX bibliographical record in XML, SIGMOD Record 27(2), June 1998
Contents

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[Abstract]
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