Fully Retroactive Approximate Range and Nearest Neighbor Searching

  • Michael T. Goodrich
  • Joseph A. Simons
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant d, a set of n points in ℝ d indexed by time such that we can perform insertions or deletions at any point in the timeline in O(logn) amortized time. We support, for any small constant ε > 0, (1 + ε)-approximate range reporting queries at any point in the timeline in O(logn + k) time, where k is the output size. We also show how to answer (1 + ε)-approximate nearest neighbor queries for any point in the past or present in O(logn) time.

Keywords

Voronoi Diagram Range Query Query Point Neighbor Query Approximate Range 
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 2011

Authors and Affiliations

  • Michael T. Goodrich
    • 1
  • Joseph A. Simons
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaIrvineUSA

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