Optimistic Imprecise Shortest Watchtower in 1.5D and 2.5D
Bradley McCoy, Binhai Zhu

TL;DR
This paper introduces a linear-time exact algorithm for the 1.5D optimistic shortest watchtower problem and an approximation scheme for the 2.5D case, optimizing watchtower placement in imprecise terrains.
Contribution
It provides the first linear-time solution for the 1.5D case and an efficient approximation scheme for the 2.5D case with bounded error.
Findings
Linear time algorithm for 1.5D case
Additive approximation scheme for 2.5D case
Solution within ε of optimal with polynomial complexity
Abstract
A 1.5D imprecise terrain is an -monotone polyline with fixed -coordinates, the -coordinate of each vertex is not fixed but is constrained to be in a given vertical interval. A 2.5D imprecise terrain is a triangulation with fixed and -coordinates, but the -coordinate of each vertex is constrained to a given vertical interval. Given an imprecise terrain with intervals, the optimistic shortest watchtower problem asks for a terrain realized by a precise point in each vertical interval such that the height of the shortest vertical line segment whose lower endpoint lies on and upper endpoint sees the entire terrain is minimized. In this paper, we present a linear time algorithm to solve the 1.5D optimistic shortest watchtower problem exactly. For the discrete version of the 2.5D case (where the watchtower must be placed on a vertex of ), and we give an…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Constraint Satisfaction and Optimization · Complexity and Algorithms in Graphs
