Pii: S0925-7721(00)00023-7
نویسنده
چکیده
It is shown that in any polygonal art gallery of n sides it is possible to place bn/3c point guards whose range of vision is 180◦ so that every interior point of the gallery can be seen by at least one of them. The guards can be stationed at any point of the art gallery. This settles an open problem posed by J. Urrutia. 2000 Elsevier Science B.V. All rights reserved.
منابع مشابه
On the number of disjoint convex quadrilaterals for a planar point set
For a given planar point set P , consider a partition of P into disjoint convex polygons. In this paper, we estimate the maximum number of convex quadrilaterals in all partitions. 2001 Elsevier Science B.V. All rights reserved.
متن کاملPii: S0925-7721(00)00010-9
We improve previous lower bounds on the number of simple polygonizations, and other kinds of crossing-free subgraphs, of a set of N points in the plane by analyzing a suitable configuration. We also prove that the number of crossing-free perfect matchings and spanning trees is minimum when the points are in convex position. 2000 Elsevier Science B.V. All rights reserved.
متن کاملDensest lattice packings of 3-polytopes
Based on Minkowski’s work on critical lattices of 3-dimensional convex bodies we present an efficient algorithm for computing the density of a densest lattice packing of an arbitrary 3-polytope. As an application we calculate densest lattice packings of all regular and Archimedean polytopes.
متن کاملPii: S0925-7721(00)00006-7
A k-set of a finite set S of points in the plane is a subset of cardinality k that can be separated from the rest by a straight line. The question of how many k-sets a set of n points can contain is a long-standing open problem where a lower bound of (n logk) and an upper bound of O(nk1/3) are known today. Under certain restrictions on the set S, for example, if all points lie on a convex curv...
متن کاملPii: S0925-7721(01)00015-3
In this paper we present a heuristic to reconstruct nonsmooth curves with multiple components. Experiments with several input data reveals the effectiveness of the algorithm in contrast with the other competing algorithms. 2001 Elsevier Science B.V. All rights reserved.
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