Guarding polyhedral terrain by k-watchtowers
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
The discrete k-watchtower problem for a polyhedral terrain (formula presented) 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 (formula presented), and every point of (formula presented) is visible from the top end-point of at least one of those vertical segments. Agarwal et al.  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 (formula presented) for a fixed constant k. Our algorithm does not use parametric search.
Tripathi, Nitesh; Pal, Manjish; De, Minati; Das, Gautam; and Nandy, Subhas C., "Guarding polyhedral terrain by k-watchtowers" (2018). Conference Articles. 156.