New data structures for orthogonal range searching

  • Authors:
  • S. Alstrup;G. Stolting Brodal;T. Rauhe

  • Affiliations:
  • -;-;-

  • Venue:
  • FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
  • Year:
  • 2000

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Abstract

We present new general techniques for static orthogonal range searching problems in two and higher dimensions. For the general range reporting problem in R/sup 3/, we achieve query time O(log n+k) using space O(n log/sup 1+/spl epsiv// n), where n denotes the number of stored points and k the number of points to be reported. For the range reporting problem on an n/spl times/n grid, we achieve query time O(log log n+k) using space O(n log/sup /spl epsiv// n). For the two-dimensional semi-group range sum problem we achieve query time O(log n) using space O(n log n).