Guarding a 1.5D terrain with Imprecise Viewpoints

Given an \(n\)-vertex 1.5D terrain \(T\) and a set of \(m\) edges of \(T\), we study the problem of placing one viewpoint on each edge so that the total length of the visible portions of the terrain is maximized. We present an \(O(n+m \log m)\) time \(1/2\)-approximation algorithm for the general problem, and polynomial-time algorithms for the cases \(m=1\) and \(m=2\). Additionally, we show that the problem of computing a point on \(T\) maximizing the visible portion of \(T\) can be solved in \(O(n^3)\) time.

This is joint work with Vahideh Keikha, Maarten Löffler and Pavel Valtr.