On k-Guarding of Polygons

نویسندگان

  • Patrice Belleville
  • Prosenjit Bose
  • Jurek Czyzowicz
  • Jorge Urrutia
  • Joseph Zaks
چکیده

A polygon is called k-guardable if it is possible to find a collection G of points in the interior of the edges of P such that every point in P is visible from at least k elements of G, and such that no edge of P contains more than one element of G. In this paper we prove that every simple polygon can be 1-guarded using at most n/2 guards, and that every polygon with 0 or 1 polygonal hole can be 2-guarded. We also prove that even though every polygon with holes is 1-guardable, for every h ≥ 2 there exists a polygon with h holes that is not 2-guardable. Our proofs lead to linear time algorithms to find 1and 2-guarding collections for polygons with 0 or 1 hole.

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تاریخ انتشار 2007