Square and Rectangle Covering with Outliers

  • Hee-Kap Ahn
  • Sang Won Bae
  • Sang-Sub Kim
  • Matias Korman
  • Iris Reinbacher
  • Wanbin Son
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5598)

Abstract

For a set of n points in the plane, we consider the axis–aligned (p,k)-Box Covering problem: Find p axis-aligned, pairwise disjoint boxes that together contain exactly n − k points. Here, our boxes are either squares or rectangles, and we want to minimize the area of the largest box. For squares, we present algorithms that find the solution in O(n + klogk) time for p = 1, and in O(nlogn + kplogpk) time for p = 2,3. For rectangles we have running times of O(n + k3) for p = 1 and O(nlogn + k2 + plogp − 1k) time for p = 2,3. In all cases, our algorithms use O(n) space.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Sang Won Bae
    • 1
  • Sang-Sub Kim
    • 1
  • Matias Korman
    • 2
  • Iris Reinbacher
    • 1
  • Wanbin Son
    • 1
  1. 1.Department of Computer Science and EngineeringPOSTECHSouth Korea
  2. 2.Graduate School of Information ScienceTohoku UniversityJapan

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