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Indexed Geometric Jumbled Pattern Matching

  • Stephane Durocher
  • Robert Fraser
  • Travis Gagie
  • Debajyoti Mondal
  • Matthew Skala
  • Sharma V. Thankachan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8486)

Abstract

We consider how to preprocess n colored points in the plane such that later, given a multiset of colors, we can quickly find an axis-aligned rectangle containing a subset of the points with exactly those colors, if one exists. We first give an index that uses o(n 4) space and o (n) query time when there are \({\mathcal{O}({1})}\) distinct colors. We then restrict our attention to the case in which there are only two distinct colors. We give an index that uses \({\mathcal{O}({n})}\) bits and \({\mathcal{O}({1})}\) query time to detect whether there exists a matching rectangle. Finally, we give a \({\mathcal{O}({n})}\)-space index that returns a matching rectangle, if one exists, in \({\mathcal{O}({\lg ^2 n / \lg \lg n})}\) time.

Keywords

Binary Search Binary String Query Time Distinct Color Connected Subgraph 
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 International Publishing Switzerland 2014

Authors and Affiliations

  • Stephane Durocher
    • 1
  • Robert Fraser
    • 1
  • Travis Gagie
    • 2
  • Debajyoti Mondal
    • 1
  • Matthew Skala
    • 1
  • Sharma V. Thankachan
    • 3
  1. 1.Department of Computer ScienceUniversity of ManitobaCanada
  2. 2.Department of Computer ScienceUniversity of HelsinkiFinland
  3. 3.Cheriton School of Computer ScienceUniversity of WaterlooCanada

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