We obtain a polynomial time approximation scheme for the terrain guarding problem improving upon several recent constant factor approximations. Our algorithm is a local search algorithm inspired byâ€¦ (More)

Given a metric <i>d</i> defined on a set <i>V</i> of points (a metric space), we define the ball B(<i>v, r</i>) centered at <i>u</i> âˆˆ <i>V</i> and having radius <i>r</i> â‰¥ 0 to be the set {<i>q</i>â€¦ (More)

We obtain a polynomial time approximation scheme for the 1.5D terrain guarding problem, improving upon several recent constant factor approximations. Our algorithm is a local search algorithmâ€¦ (More)

A polygon P is x-monotone if any line orthogonal to the x-axis has a simply connected intersection with P . A set G of points inside P or on the boundary of P is said to guard the polygon if everyâ€¦ (More)

In this paper, we give a characterization of the visibility graphs of pseudo-polygons. We first identify some key combinatorial properties of pseudo-polygons, and we then give a set of five necessaryâ€¦ (More)

We show that vertex guarding a monotone polygon is NP-hard and construct a constant factor approximation algorithm for interior guarding monotone polygons. Using this algorithm we obtain anâ€¦ (More)