On Guarding Orthogonal Polygons with Sliding Cameras

TL;DR

This paper introduces a constant-factor approximation algorithm for guarding orthogonal polygons with sliding cameras, explores efficient solutions based on dual graph properties, and establishes bounds relating the number of guards to polygon vertices.

Contribution

It presents the first constant-factor approximation algorithm for sliding camera guarding, analyzes linear-time solvability with bounded treewidth, and provides art gallery bounds for sliding cameras.

Findings

First constant-factor approximation algorithm for sliding cameras.

Linear-time solvability when dual graph has bounded treewidth.

Bounds on number of guards relative to polygon vertices.

Abstract

A sliding camera inside an orthogonal polygon $P$ is a point guard that travels back and forth along an orthogonal line segment $\gamma$ in $P$. The sliding camera $g$ can see a point $p$ in $P$ if the perpendicular from $p$ onto $\gamma$ is inside $P$. In this paper, we give the first constant-factor 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. Finally, we study art gallery theorems for sliding cameras, thus, give upper and lower bounds in terms of the number of guards needed relative to the number of vertices $n$.