A Self-Stabilizing K-Clustering Algorithm Using an Arbitrary Metric (Revised Version of RR2008-31)

Eddy Caron (1) , Ajoy Datta (2) , Benjamin Depardon (1) , Lawrence Larmore (2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 Department of Computer Science [Las Vegas]

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 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(log n + log k) space per process, where n is the size of the network. This is the first distributed solution to the k-clustering problem on weighted graphs.

Keywords: K-Clustering; Self-Stabilization; Weighted Graph

Domains: Computer Science [cs]; Distributed, Parallel, and Cluster Computing [cs.DC]

Eddy Caron, Ajoy Datta, Benjamin Depardon, Lawrence Larmore. A Self-Stabilizing K-Clustering Algorithm Using an Arbitrary Metric (Revised Version of RR2008-31). 2009. ⟨ensl-00440266⟩