A self-stabilizing kk-clustering algorithm for weighted graphs

Mobile ad hoc   networks as well as grid platforms are distributed, changing, and error prone environments. Communication costs within such infrastructure can be improved, or at least bounded, by using kk-clustering  . A kk-clustering of a graph, is a partition of the nodes into disjoint sets, called clusters, in which every node is distance at most kk from a designated node in its cluster, called the clusterhead  . A self-stabilizing asynchronous distributed algorithm is given for constructing a kk-clustering of a connected network of processes with unique IDs and weighted edges. The algorithm is comparison based, takes O(nk)O(nk) time, and uses O(logn+logk)O(logn+logk) space per process, where nn is the size of the network. To the best of our knowledge, this is the first solution to the kk-clustering problem on weighted graphs.

Research highlights
► kk-clustering: Creation of clusters of diameter at most 2k2k.
► Self-stabilizing algorithm under an unfair daemon.
► The algorithm takes O(nk)O(nk) rounds to converge.
► Only O(logn+logk)O(logn+logk) memory is required.