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Maximum-Width Empty Square and Rectangular Annulus

  • Sang Won BaeEmail author
  • Arpita Baral
  • Priya Ranjan Sinha Mahapatra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11355)

Abstract

An annulus is, informally, a ring-shaped region, often described by two concentric circles. The maximum-width empty annulus problem asks to find an annulus of a certain shape with the maximum possible width that avoids a given set of n points in the plane. This problem can also be interpreted as the problem of finding an optimal location of a ring-shaped obnoxious facility among the input points. In this paper, we study square and rectangular variants of the maximum-width empty anuulus problem, and present first nontrivial algorithms. Specifically, our algorithms run in \(O(n^3)\) and \(O(n^2 \log n)\) time for computing a maximum-width empty axis-parallel square and rectangular annulus, respectively. Both algorithms use only O(n) space.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sang Won Bae
    • 1
    Email author
  • Arpita Baral
    • 2
  • Priya Ranjan Sinha Mahapatra
    • 2
  1. 1.Division of Computer Science and EngineeringKyonggi UniversitySuwonRepublic of Korea
  2. 2.Department of Computer Science and EngineeringUniversity of KalyaniKalyaniIndia

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