Guarding lines and 2-link polygons is apx-hard
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چکیده
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Fast Vertex Guarding for Polygons
For a polygon P with n vertices, the vertex guarding problem asks for the minimum subset G of P ’s vertices such that every point in P is seen by at least one point in G. This problem is NP-complete and APX-hard. The first approximation algorithm (Ghosh, 1987) involves decomposing P into O ( n ) cells that are equivalence classes for visibility from the vertices of P . This discretized problem ...
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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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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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Given a set P of n points in the plane, Covering Points by Lines is the problem of finding a minimum-cardinality set L of lines such that every point p ∈ P is incident to some line l ∈ L. As a geometric variant of Set Cover, Covering Points by Lines is still NP-hard. Moreover, it has been proved to be APX-hard, and hence does not admit any polynomial-time approximation scheme unless P = NP. In ...
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The art gallery problem enquires about the least number of guards sufficient to ensure that an art gallery, represented by a polygon P , is fully guarded. Most standard versions of this problem are known to be NP-hard. In 1987, Ghosh provided a deterministic O(log n)approximation algorithm for the case of vertex guards and edge guards in simple polygons. In the same paper, Ghosh also conjecture...
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