New findings on the complexity of cluster head selection algorithms

Clustering schemes offer a practical way of providing scalability when dealing with large and dense Mobile Ad hoc Networks (MANETs). The feasibility of clustering can be determined by the complexity of the cluster head selection. Optimizing the cluster head selection allows for the network to be more efficient by minimizing the signaling overhead while ensuring that the network connectivity is maintained despite topology changes. In this paper, we present some new findings on the complexity of the cluster head selection algorithms. Two variants of the cluster head selection are examined: (1) the distance-constrained selection where every node in the network must be located within a certain distance to the nearest cluster head; and (2) the size-constrained selection where each cluster is only allowed to have a limited number of members. We show that the problem of minimizing the set of cluster heads is NP-hard for both variants. We propose two distributed selection algorithms, each having logarithmic approximation ratio, for these variants. We also discuss, using NS-2 simulations, the resulting cluster size distribution and cluster head density, which impact the efficient operation of the network.