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Computing the k-Crossing Visibility Region of a Point in a Polygon

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Combinatorial Algorithms (IWOCA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11638))

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Abstract

Two points p and q in a simple polygon P are k-crossing visible when the line segment pq crosses the boundary of P at most k times. Given a query point q, an integer k, and a polygon P, we propose an algorithm that computes the region of P that is k-crossing visible from q in O(nk) time, where n denotes the number of vertices of P. This is the first such algorithm parameterized in terms of k, resulting in asymptotically faster worst-case running time relative to previous algorithms when k is \(o(\log {n})\), and bridging the gap between the O(n)-time algorithm for computing the 0-visibility region of q in P and the \(O(n\log n)\)-time algorithm for computing the k-crossing visibility region of q in P.

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Notes

  1. 1.

    All indices are computed modulo the size of the corresponding vertex set: \(m+1\) in this case.

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Authors and Affiliations

  1. University of Manitoba, Winnipeg, Canada

    Yeganeh Bahoo & Stephane Durocher

  2. Carleton University, Ottawa, Canada

    Prosenjit Bose

  3. Simon Fraser University, Burnaby, Canada

    Thomas Shermer

Authors
  1. Yeganeh Bahoo
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  2. Prosenjit Bose
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  3. Stephane Durocher
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  4. Thomas Shermer
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Corresponding authors

Correspondence to Yeganeh Bahoo , Prosenjit Bose , Stephane Durocher or Thomas Shermer .

Editor information

Editors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Charles J. Colbourn

  2. University of Pisa, Pisa, Italy

    Roberto Grossi

  3. University of Pisa, Pisa, Italy

    Nadia Pisanti

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Bahoo, Y., Bose, P., Durocher, S., Shermer, T. (2019). Computing the k-Crossing Visibility Region of a Point in a Polygon. In: Colbourn, C., Grossi, R., Pisanti, N. (eds) Combinatorial Algorithms. IWOCA 2019. Lecture Notes in Computer Science(), vol 11638. Springer, Cham. https://doi.org/10.1007/978-3-030-25005-8_2

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  • DOI: https://doi.org/10.1007/978-3-030-25005-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-25004-1

  • Online ISBN: 978-3-030-25005-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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