Stabbing segments with rectilinear objects

Mercè Claverol, Delia Garijo, Matias Korman, Carlos Seara, Rodrigo I. Silveira

Research output: Contribution to journalArticlepeer-review

Abstract

Given a set S of n line segments in the plane, we say that a region R⊆R2 is a stabber for S if R contains exactly one endpoint of each segment of S. In this paper we provide optimal or near-optimal algorithms for reporting all combinatorially different stabbers for several shapes of stabbers. Specifically, we consider the case in which the stabber can be described as the intersection of axis-parallel halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). The running times are O(n) (for the halfplane case), O(nlog n) (for strips, quadrants, and 3-sided rectangles), and O(n2log n) (for rectangles).

Original languageEnglish
Pages (from-to)359-373
Number of pages15
JournalApplied Mathematics and Computation
Volume309
DOIs
Publication statusPublished - 2017 Sep 15

Keywords

  • Algorithms
  • Classification problems
  • Computational geometry
  • Line segments
  • Stabbing problems

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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