A distributed counting architecture for exploring the structure of anonymous active–passive networks

Abstract

Active–passive networks are composed of nodes that meet specific criteria depending on applications (active nodes) and nodes that do not (passive nodes). This paper investigates the network size estimation problem, which involves determining the number of active nodes in anonymous active–passive networks in a distributed way. To this end, a distributed counting architecture is proposed to locally manipulate the criteria for being an active node via a variable and to count the number of active nodes, where this is accomplished without prior knowledge of the network or a procedure for initialization. Several properties of an anonymous network such as network size, number of nodes for a given degree, the maximum and minimum degrees, and so on, can be deduced using the proposed architecture by varying the criteria variable. Stability and convergence analysis of the proposed architecture are presented, and its effectiveness is also demonstrated through a numerical example.