An ad hoc network may be logically represented as a set of clusters. The clusterheads form a d-hop dominating set. Each node is at most d hops from a clusterhead. Clusterheads form a virtual backbone and may be used to route packets for nodes in their cluster. Previous heuristics restricted themselves to 1-hop clusters. We show that the minimum d-hop dominating set problem is NP-complete. Then we present a heuristic to form d-clusters in a wireless ad hoc network. Nodes are assumed to have a non-deterministic mobility pattern. Clusters are formed by diffusing node identities along the wireless links. When the heuristic terminates, a node either becomes a clusterhead, or is at most d wireless hops away from its clusterhead. The value of d is a parameter of the heuristic. The heuristic can be run either at regular intervals, or whenever the network configuration changes. One of the features of the heuristic is that it tends to re-elect existing clusterheads even when the network configuration changes. This helps to reduce the communication overheads during transition from old clusterheads to new clusterheads. Also, there is a tendency to evenly distribute the mobile nodes among the clusterheads, and evently distribute the responsibility of acting as clusterheads among all nodes. Thus, the heuristic is fair and stable. Simulation experiments demonstrate that the proposed heuristic is better than the two earlier heuristics, namely the LCA and degree-based solutions.
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