Approximability of guarding weak visibility polygons
نویسندگان
چکیده
منابع مشابه
Approximability of guarding weak visibility polygons
The art gallery problem enquires about the least number of guards that are sufficient to ensure that an art gallery, represented by a polygon P , is fully guarded. In 1998, the problems of finding the minimum number of point guards, vertex guards, and edge guards required to guard P were shown to be APX-hard by Eidenbenz, Widmayer and Stamm. In 1987, Ghosh presented approximation algorithms for...
متن کاملVertex Guarding in Weak Visibility Polygons
The art gallery problem enquires about the least number of guards that are sufficient to ensure that an art gallery, represented by a polygon P , is fully guarded. In 1998, the problems of finding the minimum number of point guards, vertex guards, and edge guards required to guard P were shown to be APX-hard by Eidenbenz, Widmayer and Stamm. In 1987, Ghosh presented approximation algorithms for...
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We are interested in the problem of guarding simple orthogonal polygons with the minimum number of r-guards. The interior point p belongs an orthogonal polygon P is visible from r-guard g, if the minimum area rectangle contained p and q lies within P . A set of point guards in polygon P is named guard set (as denoted G) if the union of visibility areas of these point guards be equal to polygon ...
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In this paper, we consider the problem of computing the weak visibility (WV ) of a query line segment inside a simple polygon. Our algorithm first preprocesses the polygon and creates data structures from which any WV query is answered efficiently in an output sensitive manner. In our solution, the preprocessing is performed in time O(n log n) and the size of the constructed data structure is O...
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For a simple polygon P of size n, we define weak visibility counting problem (WVCP) as finding the number of visible segments of P from a query line segment pq. We present different algorithms to compute WVCP in sub-linear time. In our first algorithm, we spend O(n) time to preprocess the polygon and build a data structure of size O(n), so that we can optimally answer WVCP in O(log n) time. The...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2017
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.12.015