Less restrictive knowledge connectivity condition for achieving consensus with unknown participants

For self-organised networks, neither the identity nor the number of processes is known to all participants at the beginning of the computation because no central authority exists to support such context information. Hence, achieving consensus in such networks cannot be accomplished in the ways for traditional fixed networks. In the literature, the consensus problem has been studied in a new computational model corresponding to self-organised networks. Such a variant of the traditional consensus problem is called `consensus with unknown participants` (CUP). Particularly, the CUP problem relaxes the requirement for the original knowledge owned by every process about participants in the computation. Moreover, the aforementioned work considers asynchronous networks without process crashes, and has determined the necessary and sufficient knowledge connectivity condition for solving the CUP problem, which is called `one sink reducibility` (OSR). In this study, we investigate the possibility of finding a less restrictive knowledge connectivity condition than OSR, based on which, consensus can still be achieved in self-organised networks. We demonstrate that with some certain global information inherently required for solving the CUP problem, such a possibility really exists.