Fault-Tolerant Gathering of Mobile Robots with Weak Multiplicity Detection

TL;DR

This paper presents fault-tolerant algorithms for gathering mobile robots with weak multiplicity detection, demonstrating minimal capabilities needed and introducing an intermediate asynchronous model for improved fault tolerance.

Contribution

It introduces a wait-free gathering algorithm under weak multiplicity detection in semi-synchronous and a new intermediate ASYNC_IC model for asynchronous settings, handling up to nearly half the robots being faulty.

Findings

Gathering is possible with minimal multiplicity detection capabilities.

The proposed algorithms tolerate up to n-1 and approximately n/2 faulty robots.

An intermediate asynchronous model enhances fault-tolerant gathering capabilities.

Abstract

There has been a wide interest in designing distributed algorithms for tiny robots. In particular, it has been shown that the robots can complete certain tasks even in the presence of faulty robots. In this paper, we focus on gathering of all non-faulty robots at a single point in presence of faulty robots. We propose a wait-free algorithm (i.e., no robot waits for other robot and algorithm instructs each robot to move in every step, unless it is already at the gathering location), that gathers all non-faulty robots in semi-synchronous model without any agreement in the coordinate system and with weak multiplicity detection (i.e., a robot can only detect that either there is one or more robot at a location) in the presence of at most $n-1$ faulty robots for $n\geqslant 3$. We show that the required capability for gathering robots is minimal in the above model, since relaxing it further makes gathering impossible to solve. Also, we introduce an intermediate scheduling model \textit{ASYNC$_{IC}$} between the asynchronous ( i.e., no instantaneous movement or computation) and the semi-synchronous (i.e., both instantaneous movement and computation) as the asynchronous model with instantaneous computation. Then we propose another algorithm in \textit{ASYNC$_{IC}$} model for gathering all non-faulty robots with weak multiplicity detection without any agreement on the coordinate system in the presence of at most $\lfloor n/2\rfloor-2$ faulty robots for $n\geqslant 7$.