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Enabling high-dimensional range queries using kNN indexing techniques: approaches and empirical results

Author

Listed:
  • Tim Wylie

    (University of Texas - Rio Grande Valley)

  • Michael A. Schuh

    (Montana State University)

  • Rafal A. Angryk

    (Georgia State University)

Abstract

Many modern search applications are high-dimensional and depend on efficient orthogonal range queries. These applications span web-based and scientific needs as well as uses for data mining. Although k-nearest neighbor queries are becoming increasingly common due to mobile and geospatial applications, orthogonal range queries in high-dimensional data remain extremely important and relevant. For efficient querying, data is typically stored in an index optimized for either kNN or range queries. This can be problematic when data is optimized for kNN retrieval and a user needs a range query or vice versa. Here, we address the issue of using a kNN-based index for range queries, as well as outline the general computational geometry problem of adapting these systems to range queries. We refer to these methods as space-based decompositions and provide a straightforward heuristic for this problem. Using iDistance as our applied kNN indexing technique, we also develop an optimal (data-based) algorithm designed specifically for its indexing scheme. We compare this method to the suggested naïve approach using real world datasets. The data-based algorithm consistently performs better.

Suggested Citation

  • Tim Wylie & Michael A. Schuh & Rafal A. Angryk, 2016. "Enabling high-dimensional range queries using kNN indexing techniques: approaches and empirical results," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1107-1132, November.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:4:d:10.1007_s10878-015-9927-1
    DOI: 10.1007/s10878-015-9927-1
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    References listed on IDEAS

    as
    1. Zhixiang Chen & Bin Fu & Yong Tang & Binhai Zhu, 2006. "A PTAS for a disc covering problem using width-bounded separators," Journal of Combinatorial Optimization, Springer, vol. 11(2), pages 203-217, March.
    2. Yiping Lu & Danny Z. Chen & Jianzhong Cha, 2015. "Packing cubes into a cube is NP-complete in the strong sense," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 197-215, January.
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