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Pyramid Technique

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Encyclopedia of GIS

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Synonyms

Pyramid tree

Definition

The Pyramid Technique [1] is an indexing technique for point data (feature vectors) of a multidimensional space, particularly designed for medium to high dimensionality starting from d = 10. Like Z-ordering [2] and other space-filling-curve techniques the pyramid technique gives a one‐dimensional embedding of the high dimensional points. The embedded objects can be indexed by any one‐dimensional index structure which supports range queries (interval queries) such as all B-tree [3] variants as well as all order preserving hashing methods. The pyramid technique can efficiently handle multidimensional interval queries and nearest neighbor queries using maximum metric.

Historical Background

Index structures for vector spaces of medium to high dimensionality [4,5,6] have become very popular in the 1990s, because traditional index structures for vector data, such as the R-tree [7] and its variants tend to deteriorate as the dimensionality of the space...

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Recommended Reading

  1. Berchtold, S., Böhm, C., Kriegel, H-P.: The pyramid-technique: towards breaking the curse of dimensionality, pp. 142–153, SIGMOD Conference, (1998)

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  3. Bayer, R., McCreight, E.M.: Organization and maintenance of large ordered indexes, pp. 107–141, SIGFIDET Workshop (1970)

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  4. Lin, K-I., Jagadish, H.V., Faloutsos, C.: The TV-tree: An index structure for high-dimensional data. VLDB J. 3(4):517–542 (1994) [DBLP:journals/vldb/LinJF94]

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  6. Berchtold, S., Keim, D.A., Kriegel, H-P.: The X-tree: An index structure for high-dimensional data. VLDB, 28–39 (1996)

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  7. Guttman, Aa.: R-Trees: A dynamic index structure for spatial searching. SIGMOD Conference 47–57 (1984)

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  8. Berchtold, S., Böhm, C., Keim, D.A., Kriegel, H-P.: A cost model for nearest beighbor search in high-dimensional data space. PODS 78–86 (1997)

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  9. Chang, Y.-C., Bergman, L.D., Castelli, V., Li, C.-S., Lo, M.-L., Smith, J.R.: The onion technique: indexing for linear optimization queries. SIGMOD Conference 391–402 (2000)

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  10. Ferhatosmanoglu, H., Agrawal, D., Abbadi, A.E.: Concentric hyperspaces and disk allocation for fast parallel range searching. ICDE 608–615 (1999)

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  11. Jagadish, H.V., Ooi, B.C., Tan, K.-L., Cui, Yu, Rui, Zhang: iDistance: An adaptive B+-tree based indexing method for nearest neighbor search. ACM Trans. Database Syst. 30(2):364–397 (2005)

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Author information

Authors and Affiliations

  1. Institute for Computer Science Database and Information Systems, University of Munich, Munich, Germany

    Christian Böhm

Authors
  1. Christian Böhm
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Shashi Shekhar (McKnight Distinguished University Professor) (McKnight Distinguished University Professor)

  2. Management Science and Information Systems Department, Rutgers Business School Newark and New Brunswick Rutgers, the State University of New Jersey, Newark, NJ, 07102, USA

    Hui Xiong (Assistant Professor) (Assistant Professor)

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© 2008 Springer-Verlag

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Böhm, C. (2008). Pyramid Technique. In: Shekhar, S., Xiong, H. (eds) Encyclopedia of GIS. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35973-1_1050

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