K-clustering in wireless ad hoc networks

Ad hoc networks consist of wireless hosts that communicate with each other in the absence of a fixed infrastructure. Clustering is commonly used in order to limit the amount of routing information stored and maintained at individual hosts. A k-clustering is a framework in which the wireless network is divided into non-overlapping sub networks, also referred to as clusters, and where every two wireless hosts in a sub network are at most k hops from each other. The algorithmic complexity of k-clustering is known to be NP-Complete for simple undirected graphs. For the special family of graphs that represent ad hoc wireless networks, modeled as unit disk graphs, we introduce a two phase distributed polynomial time and message complexity approximation solution with O(k) worst case ratio over the optimal solution. The first phase constructs a spanning tree of the network and the second phase then partitions the spanning tree into subtrees with bounded diameters.