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Abstract: We study the problem of minimizing the number of guards positioned at a fixed height h such that each triangle on a given 2.5dimensional triangulated terrain T is completely visible from at least one guard. We prove this problem to be NP-hard, and we show that it cannot be approximated by a polynomial time algorithm within a ratio of (1 \Gamma ffl) 35 ln n for any ffl ? 0, unless NP ` TIME(n ), where n is the number of triangles in the terrain. Since there exists an approximation... (Update)
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BibTeX entry: (Update)
St. Eidenbenz, Ch. Stamm, P. Widmayer; Positioning guards at fixed height above a terrain - an optimum inapproximability result; to appear in Proceedings of the European Symposium on Algorithms ESA, 1998. http://citeseer.ist.psu.edu/eidenbenz98positioning.html More
@inproceedings{ eidenbenz98positioning,
author = "Stephan Eidenbenz and Christoph Stamm and Peter Widmayer",
title = "Positioning Guards at Fixed Height Above a Terrain - An Optimum Inapproximability Result",
booktitle = "European Symposium on Algorithms",
pages = "187-198",
year = "1998",
url = "citeseer.ist.psu.edu/eidenbenz98positioning.html" }
Citations (may not include all citations):9 Computing the Shortest Watchtower of a Polyhedral Terrain in.. (context) - Zhu - 1997
6 Recent Results in Art Galleries; Proc (context) - Shermer - 1992
6 Art Gallery Theorems and Algorithms; Oxford University Press (context) - O'Rourke - 1987
5 Guarding Art Galleries - Methods for Mobile Guards; doctoral.. (context) - Nilsson - 1994
4 Guarding Polyhedral Terrains; Computational Geometry (context) - Bose, Shermer et al. - 1997
4 Art Gallery and Illumination Problems; to appear in Handbook.. (context) - Urrutia - 1998
3 for Approximating Set Cover; STOC (context) - Feige, of - 1996
2 Optimal Guarding of Polygons and Monotone Chains (context) - Chen, Estivill-Castro et al. - 1995
2 Digital Elevation Models and TIN Algorithms; in Algorithmic .. (context) - van Kreveld - 1997
1 Inapproximability of Some Art Gallery Problems; manuscript (context) - Eidenbenz, Stamm et al. - 1998
The graph only includes citing articles where the year of publication is known.
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