Abstract
We study the problem of minimizing the number of guards positioned at a fixed height h such that each triangle on a given 2.5-dimensional 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 − ε) 351 ln n for any ε > 0, unless NP \( \subseteq \) TIME(n O(log log n)), where n is the number of triangles in the terrain. Since there exists an approximation algorithm that achieves an approximation ratio of ln n+1, our result is close to the optimum hardness result achievable for this problem.
This work is partially supported by the Swiss National Science Foundation
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© 1998 Springer-Verlag Berlin Heidelberg
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Eidenbenz, S., Stamm, C., Widmayer, P. (1998). Positioning Guards at Fixed Height Above a Terrain — An Optimum Inapproximability Result. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_16
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DOI: https://doi.org/10.1007/3-540-68530-8_16
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