Finding the Shortest Watchman Route in a Simple Polygon
نویسندگان
چکیده
منابع مشابه
Finding the Shortest Watchman Route in a Simple Polygon
We present the rst polynomial-time algorithm that nds the shortest route in a simple polygon such that all points of the polygon are visible from the route. This route is called the shortest watchman route, and we do not assume any restrictions on the route or on the simple polygon. Our algorithm runs in worst case O(n 6) time, but it is adaptive making it run faster on polygons with simple str...
متن کاملWatchman route in a simple polygon with a rubberband algorithm
So far, the best result in running time for solving the fixed watchman route problem (i.e., shortest path for viewing any point in a simple polygon with given start point) is O(n log n), published in 2003 by M. Dror, A. Efrat, A. Lubiw, and J. Mitchell. – This paper provides an algorithm with κ(ε) · O(kn) runtime, where n is the number of vertices of the given simple polygon Π, and k the number...
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There are many di-erent kinds of guards in a simple polygon that have been proposed and discussed. In this paper, we consider a new type of guard, boundary guard, which is a guard capable of moving along a boundary of a polygon and every interior point of the polygon can be seen by the mobile guard. We propose an algorithm to 1nd the shortest boundary guard of a simple polygon P in O(n log n) t...
متن کاملAn Approximation Algorithm for the Two-Watchman Route in a Simple Polygon
The two-watchman route problem is that of computing a pair of closed tours in an environment so that the two tours together see the whole environment and some length measure on the two tours is minimized. Two standard measures are: the minmax measure, where we want the tours where the longest of them has minimal length, and the minsum measure, where we want the tours for which the sum of their ...
متن کاملEuclidean Shortest Paths in a Simple Polygon
Let p and q be two points in a simple polygon Π. This chapter provides two rubberband algorithms for computing a shortest path between p and q that is contained in Π. The two algorithms use previously known results on triangular or trapezoidal decompositions of simple polygons, and have either O (n) or O (n log n) time complexity (where the super-linear time complexity is only due to preprocess...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1999
ISSN: 0179-5376
DOI: 10.1007/pl00009467