Self-stabilizing gathering with strong multiplicity detection

In this paper, we investigate the possibility to deterministically solve the gathering problem starting from an arbitrary configuration with weak robots, i.e., anonymous, autonomous, disoriented, oblivious, and devoid of means of communication. By starting from an arbitrary configuration, we mean that robots are not required to be located at distinct positions in the initial configuration. We introduce strong multiplicity detection as the ability for the robots to detect the exact number of robots located at a given position. We show that with strong multiplicity detection, there exists a deterministic algorithm solving the gathering problem starting from an arbitrary configuration for n robots if, and only if, n is odd.