A Note on Approximating 2-Transmitters

TL;DR

This paper presents a 2-approximation algorithm for optimally placing 2-transmitters in monotone orthogonal polygons, improving efficiency in guarding such polygons with minimal transmitters.

Contribution

It introduces the first 2-approximation algorithm for guarding monotone orthogonal polygons using 2-transmitters, advancing computational geometry methods.

Findings

The algorithm guarantees a solution within twice the optimal number of transmitters.

It effectively handles the geometric constraints of orthogonal polygons.

The approach improves upon previous approximation ratios for similar guarding problems.

Abstract

A k-transmitter in a simple orthogonal polygon P is a mobile guard that travels back and forth along an orthogonal line segment s inside P. The k-transmitter can see a point p in P if there exists a point q on s such that the line segment pq is normal to s and pq intersects the boundary of P in at most k points. In this paper, we give a 2-approximation algorithm for the problem of guarding a monotone orthogonal polygon with the minimum number of 2-transmitters.