Abstract
The discrete k-watchtower problem for a polyhedral terrain \(\mathcal{T}\) with n vertices is to find k vertical segments, called watchtowers, of smallest common height, whose bottom end-points (bases) lie on some vertices of \(\mathcal{T}\), and every point of \(\mathcal T\) is visible from the top end-point of at least one of those vertical segments. Agarwal et al. [1] proposed a polynomial time algorithm using parametric search technique for this problem with \(k=2\). Surprisingly, no result is known for the problem when \(k>2\). In this paper, we propose an easy to implement algorithm to solve k-watchtower problem in \(\mathbb {R}^3\) for a fixed constant k. Our algorithm does not use parametric search.
M. De—Supported by DST-INSPIRE Faculty Grant (DST-IFA14-ENG-75).
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The authors wish to acknowledge anonymous reviewer for useful comments on the previous version of the paper.
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Tripathi, N., Pal, M., De, M., Das, G., Nandy, S.C. (2018). Guarding Polyhedral Terrain by k-Watchtowers. In: Chen, J., Lu, P. (eds) Frontiers in Algorithmics. FAW 2018. Lecture Notes in Computer Science(), vol 10823. Springer, Cham. https://doi.org/10.1007/978-3-319-78455-7_9
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DOI: https://doi.org/10.1007/978-3-319-78455-7_9
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