Gathering of mobile robots with weak multiplicity detection in presence of crash-faults

We study the Gathering problem for mobile robots in presence of faults. In classical gathering, robots gather at a point not known a priori in finite time. In this paper, we focus on gathering of all non-faulty robots at a single point in the presence of faulty robots. We propose a wait-free algorithm (i.e., no robot waits for other robot and the 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 in the coordinate system and with weak multiplicity detection (i.e., a robot can only detect that either there is one or more robots at a location) in the presence of at most [Formula presented] faulty robots for [Formula presented]. 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 a scheduling model as the asynchronous model with instantaneous computation (ASYNC[Formula presented]), which lies in between the asynchronous and the semi-synchronous model. Then we propose another algorithm in the ASYNC[Formula presented] model for gathering all non-faulty robots with weak multiplicity detection and without any agreement on the coordinate system in the presence of at most [Formula presented] faulty robots for [Formula presented].