Searching a polygonal region from the boundary

Ichiro Suzuki, Yuichi Tazoe, Masafumi Yamashita, Tiko Kameda

研究成果: ジャーナルへの寄稿学術誌査読

22 被引用数 (Scopus)


Polygon search is the problem of finding mobile intruders who move unpredictably in a polygonal region, using one or more mobile searchers. Different levels of vision are assumed to model the ability of the searchers. In this paper we mainly consider a special case of this problem, termed boundary search, in which a single searcher has to find the intruders from the boundary of the region. Our main result is that a single searcher whose vision is limited to the ray of a single flashlight is just as capable as a single searcher having a light bulb that gives 360° vision, that is, any polygon that can be searched by the latter from the boundary can also be searched by the former from the boundary. The proof of the equivalence uses another new result, termed Monotonic Extension Theorem, together with a two-dimensional diagram called the planar boundary visibility map that represents the status of the search as a function of time. We partially settle a long-standing conjecture on the equivalence of the abilities of two types of searchers, one having two flashlights and the other having full 360° vision, for the general (non-boundary) polygon search problem.

ジャーナルInternational Journal of Computational Geometry and Applications
出版ステータス出版済み - 10月 2001

!!!All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • 幾何学とトポロジー
  • 計算理論と計算数学
  • 計算数学
  • 応用数学


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