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• W2950366207 abstract "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 vertex guards and edge guards that achieved a ratio of $mathcal{O}(log n)$, which was improved upto $mathcal{O}(loglog OPT)$ by King and Kirkpatrick in 2011. It has been conjectured that constant-factor approximation algorithms exist for these problems. We settle the conjecture for the special class of polygons that are weakly visible from an edge and contain no holes by presenting a 6-approximation algorithm for finding the minimum number of vertex guards that runs in $mathcal{O}(n^2)$ time. On the other hand, for weak visibility polygons with holes, we present a reduction from the Set Cover problem to show that there cannot exist a polynomial time algorithm for the vertex guard problem with an approximation ratio better than $frac{1-epsilon}{12} ln n$ for any $epsilon > 0$, unless NP = P." @default.
• W2950366207 created "2019-06-27" @default.
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• W2950366207 date "2014-09-16" @default.
• W2950366207 modified "2023-09-27" @default.
• W2950366207 title "Vertex Guarding in Weak Visibility Polygons" @default.
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• W2950366207 hasPublicationYear "2014" @default.
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