On the optimal clustering in mobile ad hoc networks

A mobile ad hoc network (MANET) can be represented by a set of logical clusters with clusterheads (CHs) acting like virtual base-stations, hence forming a wireless virtual backbone. The role of clusterhead is a temporary one, which changes dynamically as the topology or other factors affecting it change. Finding the minimal set of CHs is an NP-complete problem. We study the performance tradeoffs between two clustering approaches. The first one is a simple clustering strategy, called virtual grid architecture (VGA), which is based on a fixed rectilinear virtual topology, while the second one is an optimal clustering strategy. We consider homogeneous as well as heterogeneous networks. First, for homogeneous MANETs with a large number of users and under the VGA clustering approach, we derive expressions for the number of CHs, worst case path length, and average case path length. We also derive expressions for the communication overhead. Second, we develop an integer linear program (ILP) that finds the optimal number of connected CHs in small to medium sized heterogeneous MANETs. Analytical and simulation results show that our proposed clustering algorithm (VGA), although being simple, is close to optimal.