Space-efficient self-stabilizing counting population protocols on mobile sensor networks

In this study, we consider a self-stabilizing counting problem for a passively-mobile sensor network with a base station originally proposed by Beauquier et al. [13], where the base station must count the number of sensors in the network. Self-stabilizing counting means that the base station eventually counts the exact number of sensors in the system from the configuration where each sensor has an arbitrary initial state. In this paper, we focus on the space complexity of the self-stabilizing counting problem in terms of the number of sensor states. We propose two self-stabilizing counting protocols. Given a known upper bound P on the number of sensors, the first protocol performs counting using 2P sensor states and its convergence time is O(log⁡n) in fair executions, where n is the actual number of sensors. The second protocol uses only 3⋅⌈P/2⌉ sensor states but assumes the global fairness, which is an assumption stronger than the standard fairness. The best known protocol requires 4P states while the corresponding lower bound is P, so our result reduces the gap of the feasibility between P and 4P.