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Untangled Monotonic Chains and Adaptive Range Search

  • Diego Arroyuelo
  • Francisco Claude
  • Reza Dorrigiv
  • Stephane Durocher
  • Meng He
  • Alejandro López-Ortiz
  • J. Ian Munro
  • Patrick K. Nicholson
  • Alejandro Salinger
  • Matthew Skala
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5878)

Abstract

We present the first adaptive data structure for two-dimensional orthogonal range search. Our data structure is adaptive in the sense that it gives improved search performance for data with more inherent sortedness. Given n points on the plane, the linear-space data structure can answer range queries in O(logn + k + m) time, where m is the number of points in the output and k is the minimum number of monotonic chains into which the point set can be decomposed, which is \(O(\sqrt{n})\) in the worst case. Our result matches the worst-case performance of other optimal-time linear-space data structures, or surpasses them when \(k=o(\sqrt{n})\). Our data structure can also be made implicit, requiring no extra space beyond that of the data points themselves, in which case the query time becomes O(k logn + m). We present a novel algorithm of independent interest to decompose a point set into a minimum number of untangled, same-direction monotonic chains in O(kn + nlogn) time.

Keywords

Search Time Binary Search Range Query Query Time Binary Search Tree 
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 2009

Authors and Affiliations

  • Diego Arroyuelo
    • 1
  • Francisco Claude
    • 2
  • Reza Dorrigiv
    • 2
  • Stephane Durocher
    • 3
  • Meng He
    • 2
  • Alejandro López-Ortiz
    • 2
  • J. Ian Munro
    • 2
  • Patrick K. Nicholson
    • 2
  • Alejandro Salinger
    • 2
  • Matthew Skala
    • 2
    • 4
  1. 1.Yahoo! Research Latin AmericaChile
  2. 2.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada
  3. 3.Department of Computer ScienceUniversity of ManitobaWinnipegCanada
  4. 4.Department of Computer ScienceUniversity of TorontoTorontoCanada

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