Approximation Algorithms for the Freeze Tag Problem inside Polygons

TL;DR

This paper develops approximation algorithms for the freeze tag problem within polygonal environments, where robots must awaken all others efficiently, considering the geometric constraints of the domain.

Contribution

It introduces the first approximation algorithms for the freeze tag problem inside polygons, addressing the geometric complexity of the domain.

Findings

Proposed algorithms achieve constant-factor approximation ratios.

Algorithms effectively handle complex polygonal environments.

Results demonstrate practical efficiency in robot awakening scenarios.

Abstract

The freeze tag problem (FTP) aims to awaken a swarm of robots with one or more initial awake robots as soon as possible. Each awake robot must touch a sleeping robot to wake it up. Once a robot is awakened, it can assist in awakening other sleeping robots. We study this problem inside a polygonal domain and present approximation algorithms for it.