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The Colored Sector Search Tree: A Dynamic Data Structure for Efficient High Dimensional Nearest-Foreign-Neighbor Queries

  • T. Graf
  • V. Kamakoti
  • N. S. Janaki Latha
  • C. Pandu Rangan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1449)

Abstract

In this paper we present the new data structure Colored Sector Search Tree (CSST) for solving the Nearest-Foreign-Neighbor Query Problem (NFNQP): Given a set S of n colored points in ℝD, where D ≥ 2 is a constant, and a subset S′ ⊂ S stored in a CSST, for any colored query point q ∈ ℝD a nearest foreign neighbor in S′, i.e. a closest point with a different color, can be reported in O(log n(log log n)D D − 1) time w.r.t. a polyhedral distance function that is defined by a star-shaped polyhedron with O(1) vertices; note that this includes the Minkowski metrics d 1 and d . It takes a preprocessing time of O(n(log n)D D − 1) to construct the CSST. Points from S can be inserted into the set S′ and removed from S′ in O(log n(log log n)D D − 1) time. The CSST uses O(n(log n)D D − 1) space. We present an application of the data structure in the parallel simulation of solute transport in aquifer systems by particle tracking. Other applications may be found in GIS (geo information systems) and in CAD (computer aided design). To our knowledge the CSST is the first data structure to be reported for the NFNQP.

Keywords

Binary Search Query Point Neighbor Problem Colored Point Dynamic Data Structure 
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 1998

Authors and Affiliations

  • T. Graf
    • 1
  • V. Kamakoti
    • 2
  • N. S. Janaki Latha
    • 3
  • C. Pandu Rangan
    • 3
  1. 1.Research Center JülichJülichGermany
  2. 2.Institute of Mathematical SciencesCIT CampusTharamani, ChennaiIndia
  3. 3.Department of Computer Science and EngineeringIndian Institute of TechnologyMadras ChennaiIndia

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