Bounded-distance multi-clusterhead formation in wireless ad hoc networks

We present a clustering technique addressing redundancy for bounded-distance clusters, which means being able to determine the minimum number of cluster-heads per node, and the maximum distance from nodes to their cluster-heads. This problem is similar to computing a (k, r)-dominating set, (k, r)-DS, of the network. (k, r)-DS is defined as the problem of selecting a minimum cardinality vertex set D of the network such that every vertex u not in D is at a distance smaller than or equal to r from at least k vertices in D. In mobile ad hoc networks (MANETs), clusters should be computed distributively, because the topology may change frequently. We present the first centralized and distributed solutions to the (k, r)-DS problem for arbitrary topologies. The centralized algorithm computes a (k · ln Δ)-approximation, where Δ is the largest cardinality among all r-hop neighborhoods in the network. The distributed approach is extended for clustering applications, while the centralized is used as a lower bound for comparison purposes. Extensive simulations are used to compare the distributed solution with the centralized one. As a case study, we propose a novel multi-core multicast protocol that applies the distributed solution for the election of cores. The new protocol is compared against PUMA, one of the best performing multicast protocols for MANETS. Simulation results show that the new protocol outperforms PUMA on the context of static networks.