Time and message complexities of the generalized distributed mobility-adaptive clustering (GDMAC) algorithm in wireless multihop networks

Distributed mobility-adaptive clustering algorithms are used in multihop ad hoc networks to separate the nodes into logical groups and build up a hierarchical network architecture. This paper studies the convergence time and message complexity of Basagni´s generalized DMAC clustering algorithm. Our results show how many time steps and signaling messages are typically needed after a single topology change to re-achieve a stable and valid cluster structure. Furthermore, we discuss chain reactions that can occur along a path if certain conditions are fulfilled. Finally, we regard a mobile scenario in order to analyze (a) the number of signaling messages per node and time step and (b) the percentage of time steps in which the cluster structure is invalid. Our results give a qualitative insight on the behavior of clustering in ad hoc networks. In particular, they show that tuning the density of clusterheads and employing a hysteresis parameter for cluster changes can significantly improve the performance.