Searching a polygonal region from the boundary

Ichiro Suzuki, Yuichi Tazoe, Masafumi Yamashita, Tiko Kameda

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)529-553
Number of pages25
JournalInternational Journal of Computational Geometry and Applications
Volume11
Issue number5
DOIs
Publication statusPublished - Oct 1 2001

Fingerprint

Flashlights
Polygon
Visibility
Equivalence
Extension Theorem
Search Problems
Boundary Problem
Monotonic
Half line
Diagram
Vision

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

Searching a polygonal region from the boundary. / Suzuki, Ichiro; Tazoe, Yuichi; Yamashita, Masafumi; Kameda, Tiko.

In: International Journal of Computational Geometry and Applications, Vol. 11, No. 5, 01.10.2001, p. 529-553.

Research output: Contribution to journalArticle

Suzuki, Ichiro ; Tazoe, Yuichi ; Yamashita, Masafumi ; Kameda, Tiko. / Searching a polygonal region from the boundary. In: International Journal of Computational Geometry and Applications. 2001 ; Vol. 11, No. 5. pp. 529-553.
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