# Chauffeuring a Crashed Robot from a Disk

## TL;DR

This paper addresses fault-tolerant evacuation algorithms for two robots on a disk with a hidden exit, focusing on minimizing worst-case evacuation time despite crash faults and varying travel speeds.

## Contribution

It introduces algorithms for evacuating two robots with one possible crash fault, including a lower bound and analysis for different travel time ratios.

## Key findings

- Algorithms tolerate one crash fault during evacuation.
- A lower bound for evacuation time is established.
- Performance varies with travel time ratio  and crash timing.

## Abstract

Evacuation of robots from a disk has attained a lot of attention recently. We visit the problem from the perspective of fault-tolerance. We consider two robots trying to evacuate from a disk via a single hidden exit on the perimeter of the disk. The robots communicate wirelessly. The robots are susceptible to crash faults after which they stop moving and communicating. We design the algorithms for tolerating one fault. The objective is to minimize the worst-case time required to evacuate both the robots from the disk. When the non-faulty robot chauffeurs the crashed robot, it takes $\alpha \geq 1$ amount of time to travel unit distance. With this, we also provide a lower bound for the evacuation time. Further, we evaluate the worst-case of the algorithms for different values of $\alpha$ and the crash time.