Covering points by disjoint boxes with outliers

Hee Kap Ahn, Sang Won Bae, Erik D. Demaine, Martin L. Demaine, Sang Sub Kim, Matias Korman, Iris Reinbacher, Wanbin Son

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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 at least n-k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have O(n+klogk) time for p=1, and O(nlogn+kplogpk) time for p=2,3. For rectangles we get 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.

Original languageEnglish
Pages (from-to)178-190
Number of pages13
JournalComputational Geometry: Theory and Applications
Volume44
Issue number3
DOIs
Publication statusPublished - 2011 Apr
Externally publishedYes

Keywords

  • Algorithms
  • Covering
  • NP hard
  • Optimization
  • Outliers

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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