On guarding orthogonal polygons with sliding cameras

Abstract

A sliding camera inside an orthogonal polygon P is a point guard that travels back and forth along an orthogonal line segment γ in P. The sliding camera g can see a point p in P if the perpendicular from p onto γ is inside P. In this paper, we give the first constantfactor approximation algorithm for the problem of guarding P with the minimum number of sliding cameras. Next, we show that the sliding guards problem is linear-time solvable if the (suitably defined) dual graph of the polygon has bounded treewidth. On the other hand, we show that the problem is NP-hard on orthogonal polygons with holes even if only horizontal cameras are allowed. Finally, we study art gallery theorems for sliding cameras, thus, give upper and lower bounds in terms of the number of sliding cameras needed relative to the number of vertices n.