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Maximum-Width Empty Square and Rectangular Annulus

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WALCOM: Algorithms and Computation (WALCOM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11355))

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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.

S.W. Bae was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B07042755). P.R.S. Mahapatra was supported by Research Project through Department of Atomic Energy (NBHM), Government of India with Ref. No. 2/48(19)/2014/R&D-II/1045.

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Authors and Affiliations

  1. Division of Computer Science and Engineering, Kyonggi University, Suwon, Republic of Korea

    Sang Won Bae

  2. Department of Computer Science and Engineering, University of Kalyani, Kalyani, India

    Arpita Baral & Priya Ranjan Sinha Mahapatra

Authors
  1. Sang Won Bae
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  2. Arpita Baral
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  3. Priya Ranjan Sinha Mahapatra
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Correspondence to Sang Won Bae .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Guwahati, Guwahati, India

    Gautam K. Das

  2. Indian Institute of Technology Guwahati, Guwahati, India

    Partha S. Mandal

  3. Indian Statistical Institute, Kolkata, India

    Krishnendu Mukhopadhyaya

  4. Gunma University, Kiryu, Japan

    Shin-ichi Nakano

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Bae, S.W., Baral, A., Sinha Mahapatra, P.R. (2019). Maximum-Width Empty Square and Rectangular Annulus. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_6

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  • DOI: https://doi.org/10.1007/978-3-030-10564-8_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10563-1

  • Online ISBN: 978-3-030-10564-8

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