Computational geometry: an introduction
Computational geometry: an introduction
Art gallery theorems and algorithms
Art gallery theorems and algorithms
The shortest watchtower and related problems for polyhedral terrains
Information Processing Letters
Visibility problems for polyhedral terrains
Journal of Symbolic Computation
An optimal parallel algorithm for the visibility of a simple polygon from a point
Journal of the ACM (JACM)
Computational geometry in C
Computational Geometry: Theory and Applications
Computing the shortest watchtower of a polyhedral terrain in O(nlogn) time
Computational Geometry: Theory and Applications
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Three-dimensional weak visibility: complexity and applications
Theoretical Computer Science
Positioning Guards at Fixed Height Above a Terrain - An Optimum Inapproximability Result
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Computational geometry in two and a half dimensions
Computational geometry in two and a half dimensions
Efficient viewshed computation on terrain in external memory
Geoinformatica
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In this paper we study the following planar two-watchtower problem: given a terrain (X-monotone chain) T with n vertices, locate two vertical segments (watchtowers) uv and u′v′ which have to be erected on T such that every point on T is visible to the top of either watchtowers (u or u′) and the maximum height of uv, u′v′ is minimized. We present an O(n4) time algorithm to solve the discrete version of this problem when v, v′ must be on some vertices of T. Under a mild condition on solving a special cubic equation with three bounded variables in O(f3) time we can also generalize the algorithm to solve the general problem in O(n4 +n3f3) time. Using parametric search, the discrete problem can be solvedin O(n3 log2 n) time and the general problem can be solvedin O(n4 log2 n) time.