A Self-stabilizing K-Clustering Algorithm Using an Arbitrary Metric

Authors:
Eddy Caron;Ajoy K. Datta;Benjamin Depardon;Lawrence L. Larmore
Affiliations:
University of Lyon. LIP Laboratory. UMR CNRS - ENS Lyon, and - INRIA - UCBL 5668, France;University of Nevada Las Vegas, USA;University of Lyon. LIP Laboratory. UMR CNRS - ENS Lyon, and - INRIA - UCBL 5668, France;University of Nevada Las Vegas, USA
Venue:
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Year:
2009

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Abstract

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