Cooperative guards in art galleries
نویسندگان
چکیده
منابع مشابه
Guarding curvilinear art galleries with vertex or point guards
One of the earliest and most well known problems in computational geometry is the socalled art gallery problem. The goal is to compute the minimum possible number guards placed on the vertices of a simple polygon in such a way that they cover the interior of the polygon. In this paper we consider the problem of guarding an art gallery which is modeled as a polygon with curvilinear walls. Our ma...
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We consider the problem of guarding curvilinear art galleries. A closed arc a joining two points, p and q, in the plane is called a convex arc if the curve obtained by joining a with the line segment pq encloses a convex set. A piece-wise convex polygon P with vertices v0, . . . , vn−1 is the region bounded by a set {a0, . . . , an−1} of n convex arcs with pairwise disjoint interiors such that ...
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In this paper we consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves, with edge or mobile guards. Our focus is on piecewise-convex polygons, i.e., polygons that are locally convex, except possibly at the vertices, and their edges are convex arcs. We transform the problem of monitoring a piecewise-convex polygon to the problem of 2dominat...
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The Art Gallery Problem is one of the most well-known problems in Computational Geometry, with a rich history in the study of algorithms, complexity, and variants. Recently there has been a surge in experimental work on the problem. In this survey, we describe this work, show the chronology of developments, and compare current algorithms, including two unpublished versions, in an exhaustive exp...
متن کاملArt Galleries with Interior Walls
Consider an art gallery formed by a polygon on n vertices with m pairs of vertices joined by interior diagonals, the interior walls. Each interior wall has an arbitrarily placed, arbitrarily small doorway. We will show that the minimum number of guards that suffice to guard all art galleries with n vertices and m interior walls is min{b(2n−3)/3c, b(2n+m−2)/4c, b(2m+n)/3c}. If we restrict oursel...
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ژورنال
عنوان ژورنال: Dissertationes Mathematicae
سال: 2007
ISSN: 0012-3862,1730-6310
DOI: 10.4064/dm450-0-1