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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 + k p log p k) time for p = 2,3. For rectangles we have running times of O(n + k 3) for p = 1 and O(nlogn + k 2 + p log p − 1 k) time for p = 2,3. In all cases, our algorithms use O(n) space.

Keywords

Extreme Point Covering Problem Covering Algorithm Optimal Index Vertical Slab 
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

  • 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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