Improving Space Complexity of Self-stabilizing Counting on Mobile Sensor Networks

We consider a problem on a passively-mobile sensor network with a base station; the base station counts the number of sensors in the network. In [6] these passively-mobile sensor networks are modeled by extending the model of population protocols and self-stabilizing protocols to count the number of existing sensors, where self-stabilizing counting means from any initial states of sensors and some initialization of the base station (unless the base station is initialized, this problem can not be solved in general), the base station eventually counts the exact number of sensors in the system. In this setting, Beauquier et al.[6] show several protocols to solve the self-stabilizing counting (See Table 1). In this paper, we focus on space complexity of the self-stabilizing counting protocols (that is, the number of states sensors can possess, denoted by alpha(P), where P is an upper bound of the number of states) and improve it by showing self-stabilizing counting protocols using alpha(P) = 2P and alpha(P) = 3P/2, respectively. Since previous best known protocol needs alpha(P) = 4P and a lower bound of alpha(P) is P, we can shrink the gap lying that feasibility.