Computing the Smallest Color-Spanning Axis-Parallel Square

  • Payam Khanteimouri
  • Ali Mohades
  • Mohammad Ali Abam
  • Mohammad Reza Kazemi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)

Abstract

For a given set of n colored points with k colors in the plane, we study the problem of computing the smallest color-spanning axis-parallel square. First, for a dynamic set of colored points on the real line, we propose a dynamic structure with O(log2n) update time per insertion and deletion for maintaining the smallest color-spanning interval. Next, we use this result to compute the smallest color-spanning square. Although we show there could be Ω(kn) minimal color-spanning squares, our algorithm runs in O(nlog2n) time and O(n) space.

Keywords

Computational Geometry Algorithm Color-Spanning Objects 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Payam Khanteimouri
    • 1
  • Ali Mohades
    • 1
  • Mohammad Ali Abam
    • 2
  • Mohammad Reza Kazemi
    • 1
  1. 1.Tehran PolytechnicAmirkabir University of TechnologyTehranIran
  2. 2.Sharif University of TechnologyTehranIran

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