A data structure for orthogonal range queries

@article{Lueker1978ADS,
  title={A data structure for orthogonal range queries},
  author={George S. Lueker},
  journal={19th Annual Symposium on Foundations of Computer Science (sfcs 1978)},
  year={1978},
  pages={28-34}
}
  • G. S. Lueker
  • Published 16 October 1978
  • Computer Science
  • 19th Annual Symposium on Foundations of Computer Science (sfcs 1978)
Given a set of points in a d-dimensional space, an orthogonal range query is a request for the number of points in a specified d-dimensional box. [...] Key Method Next we briefly discuss decision tree bounds on the complexity of orthogonal range queries. We show that a decision tree of height O(dn log n) (Where the implied constant does not depend on d or n) can be constructed to process n operations in d dimensions. This suggests that the standard decision tree model will not provide a useful method for…Expand
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A data structure, called a priority range tree, which accommodates fast orthogonal range reporting queries on prioritized points, which is motivated by the Weber–Fechner Law, which states that humans perceive and interpret data on a logarithmic scale. Expand
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It is shown here that fi(n(logn) ~) is a lower bound on the inherent worst case time reqmred to process a sequence of n intermixed insemons, deleuons, and range queries, which imphes that the Lueker and Wdlard data structures are in some sense optimal. Expand
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A succinct representations of a d-dimensional point setsupporting orthogonal range searching under two circumstances is introduced and a succinct representation of the point set which requires dn lg U + o( n lg n) bits is proposed while supporting these queries in the same time complexity as that in rank space. Expand
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A set of “loGical structures” is described and ‘then their implementation in primary and secondary memories is discussed, and a set of algorithms for efficiently answering range queries are surveyed. Expand
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A new class of binary search trees, called trees of bounded balance, is introduced. These trees are easy to maintain in their form despite insertions and deletions of nodes, and the search time isExpand
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A multidimensional divide-and-conquer technique is employed that gives rise to a compact data structure for geometric and statistical search problems and a large number of important statistical quantities are computed much faster than was previously possible. Expand
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Classic binary search is extended to multidimensional search problems. This extension yields efficient algorithms for a number of tasks such as a secondary searching problem of Knuth, region locationExpand
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Note Added August
  • Note Added August
  • 1978
Private Communication, August 1978. Jon Bentley and Jerome Friedman, "Algorithms and Data Structures for Range Searching,
  • Proceedings of the Computer Science
  • 1978
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