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Japanese Conference on Discrete and Computational Geometry

JCDCG 2004: Discrete and Computational Geometry pp 174–183Cite as

An Optimal Algorithm for the 1-Searchability of Polygonal Rooms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3742))

Abstract

The 1-searcher is a mobile guard who can see only along a ray emanating from his position and can continuously change the direction of the ray with bounded speed. A polygonal region P with a specified point d on its boundary is called a room, and denoted by (P, d). The room (P, d) is said to be 1-searchable if the searcher, starting at the point d, can eventually see a mobile intruder who moves arbitrarily fast inside P, without allowing the intruder to touch d. We present an optimal O(n) time algorithm to determine whether there is a point x on the boundary of P such that the room (P, x) is 1-searchable. This improves upon the previous O(n log n) time bound, which was established for determining whether or not a room (P, d) is 1-searchable, where d is a given point on the boundary of P.

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Author information

Authors and Affiliations

  1. Tokai University, 317 Nishino, Numazu, 410-0395, Japan

    Xuehou Tan

Authors
  1. Xuehou Tan
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku Tokio, Japan

    Jin Akiyama

  2. Ibaraki University, Nakanarusawa, 316-8511, Hitachi, Ibaraki, Japan

    Mikio Kano

  3. Tokai University, 317 Nishino, 410-0395, Numazu, Japan

    Xuehou Tan

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© 2005 Springer-Verlag Berlin Heidelberg

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Tan, X. (2005). An Optimal Algorithm for the 1-Searchability of Polygonal Rooms. In: Akiyama, J., Kano, M., Tan, X. (eds) Discrete and Computational Geometry. JCDCG 2004. Lecture Notes in Computer Science, vol 3742. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11589440_18

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  • DOI: https://doi.org/10.1007/11589440_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30467-8

  • Online ISBN: 978-3-540-32089-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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