A (7/2)-Approximation Algorithm for Guarding Orthogonal Art Galleries with Sliding Cameras

TL;DR

This paper presents the first constant-factor approximation algorithm with a (7/2) ratio and polynomial time complexity for the minimum sliding cameras problem in orthogonal polygons, improving the efficiency of guarding strategies.

Contribution

Introduces a novel $O(n^{5/2})$-time $(7/2)$-approximation algorithm for the MSC problem in orthogonal polygons, answering an open question from prior research.

Findings

First constant-factor approximation for MSC problem

Algorithm runs in $O(n^{5/2})$ time

Achieves a (7/2)-approximation ratio

Abstract

Consider a sliding camera that travels back and forth along an orthogonal line segment $s$ inside an orthogonal polygon $P$ with $n$ vertices. The camera can see a point $p$ inside $P$ if and only if there exists a line segment containing $p$ that crosses $s$ at a right angle and is completely contained in $P$. In the minimum sliding cameras (MSC) problem, the objective is to guard $P$ with the minimum number of sliding cameras. In this paper, we give an $O(n^{5/2})$-time $(7/2)$-approximation algorithm to the MSC problem on any simple orthogonal polygon with $n$ vertices, answering a question posed by Katz and Morgenstern (2011). To the best of our knowledge, this is the first constant-factor approximation algorithm for this problem.