Fault-tolerant gathering of mobile robots with weak multiplicity detection

There has been awide 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 waitfree algorithm(i.e., no robot waits for other robots 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 the semi-synchronous model without any agreement about the coordinate system and with weak multiplicity detection (i.e., a robot can detect if there are more than one robots at a point, but not their exact number) in the presence of at most n-1 faulty robots for n ≥ 3. We show that the required capability for gathering robots is minimal in the abovemodel, since relaxing it further makes gathering impossible to solve. Also, we introduce an intermediate scheduling model in between the asynchronous (i.e., no instantaneousmovement or computation) and the semi-synchronous (i.e., both instantaneousmovement and computation) as ASYNC_IC, the asynchronous model with instantaneous computation. Then we propose another algorithm in ASYNC_IC model for gathering all non-faulty robots with weak multiplicity detection without any agreement on the coordinate systemin the presence of at most [n/2]-2 faulty robots for n ≥ 7 starting from any configuration with at most one multiplicity excluding C^•(0), C^•(1/k), C^•(1/2) and C^•(1/2+1/k).