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Finding the shortest watchman route in a simple polygon
 IN PROC. 4TH INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION, ISAAC'93
, 1993
"... We present the first polynomialtime algorithm that finds 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 algorit ..."
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Cited by 29 (3 self)
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We present the first polynomialtime algorithm that finds 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
MinimumLink Watchman Tours
, 1994
"... We consider the problem of computing a watchman route in a polygon with holes. We show that the problem of finding a minimumlink watchman route is NPcomplete, even if the holes are all convex. The proof is based on showing that the related problem of finding a minimumlink tour on a set of poin ..."
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Cited by 13 (3 self)
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We consider the problem of computing a watchman route in a polygon with holes. We show that the problem of finding a minimumlink watchman route is NPcomplete, even if the holes are all convex. The proof is based on showing that the related problem of finding a minimumlink tour on a set
Approximating the Shortest Watchman Route in a Simple Polygon
 In Proc. 4th Annu. Internat. Sympos. Algorithms Comput., volume 762 of Lecture Notes Comput. Sci
, 1993
"... We present a fast algorithm for computing a watchman route in a simple polygon that is at most a constant factor longer than the shortest watchman route. The algorithm runs in O(n log n) time as compared to the best known algorithm that computes a shortest watchman route which runs in O(n 4 ) tim ..."
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Cited by 7 (0 self)
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examples of optimization problems and in particular shortest route problems (for instance the Traveling Salesperson Problem) that are NPhard. The combined problem, to ønd the shortest closed curve (watchman route) inside a simple polygon such that each point of the polygon is visible to at least one point
Watchman Routes for Lines and Line Segments
, 2013
"... Given a set L of nonparallel lines in the plane, a watchman route (tour) for L is a closed curve contained in the union of the lines in L such that every line is visited (intersected) by the route; we similarly define a watchman route (tour) for a connected set S of line segments. The watchman rout ..."
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route problem for a given set of lines or line segments is to find a shortest watchman route for the input set, and these problems are natural special cases of the watchman route problem in a polygon with holes (a polygonal domain). In this paper, we show that the problem of computing a shortest
Approximating a Shortest Watchman Route
, 2001
"... We present a fast algorithm for computing a watchman route in a simple polygon that is at most a constant factor longer than the shortest watchman route. The algorithm runs in O(n log n) time as compared to the best known algorithm that computes a shortest watchman route which runs in O(n^6) time. ..."
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We present a fast algorithm for computing a watchman route in a simple polygon that is at most a constant factor longer than the shortest watchman route. The algorithm runs in O(n log n) time as compared to the best known algorithm that computes a shortest watchman route which runs in O(n^6) time.
Optimally Computing a Shortest Weakly Visible Line Segment Inside a Simple Polygon
 Computational Geometry: Theory and Applications
, 2002
"... A simple polygon is said to be weakly internally visible from a line segment lying inside it if every point on the boundary of the polygon is visible from some point on the line segment. In this paper, we present an optimal lineartime algorithm for the following problem: Given a simple polygon, eit ..."
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Cited by 6 (1 self)
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, either compute a shortest line segment from which the polygon is weakly internally visible, or report that the polygon is not weakly internally visible.
Watchman Routes in the Presence of a Pair of Convex Polygons
 Information Sciences
, 1995
"... Given a set of polygonal obstacles in the plane, the shortest watchman route problem asks for a closed route from which each point in the exterior of the polygons is visible to some point along the route. This problem is known to be NPhard and the development of an efficient approximation algorithm ..."
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Cited by 8 (0 self)
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Given a set of polygonal obstacles in the plane, the shortest watchman route problem asks for a closed route from which each point in the exterior of the polygons is visible to some point along the route. This problem is known to be NPhard and the development of an efficient approximation
Watchman 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 3 log n), published in 2003 by M. Dror, A. Efrat, A. Lubiw, and J. Mitchell. – This paper provides an algorithm with κ(ε) ..."
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Cited by 5 (5 self)
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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 3 log n), published in 2003 by M. Dror, A. Efrat, A. Lubiw, and J. Mitchell. – This paper provides an algorithm with κ
Watchman Route Problem
"... The Watchman Route Problem is an optimization problem in computational geometry where the objective is to compute the shortest route that a watchman should take, to guard an entire area, given only the layout of area. In the computational geometry version of the problem, the layout of the area is re ..."
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is represented by a simple polygon and the objective is to find a shortest closed curve such that all the points within the polygon and on its boundary are visible to at least one point on the curve. This report involves a study of some of the algorithms that have been proposed so far to solve this problem.
Shortest paths in simple polygons with polygonmeet constraints
, 2004
"... We study a constrained version of the shortest path problem in simple polygons, in which the path must visit a given target polygon. We provide a worstcase optimal algorithm for this problem and also present a method to construct a subdivision of the simple polygon to efficiently answer queries to ..."
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Cited by 6 (4 self)
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We study a constrained version of the shortest path problem in simple polygons, in which the path must visit a given target polygon. We provide a worstcase optimal algorithm for this problem and also present a method to construct a subdivision of the simple polygon to efficiently answer queries
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