Self-stabilizing (k,r)-Clustering in Clock Rate-Limited Systems

Wireless Ad-hoc networks are distributed systems that often reside in error-prone environments. Self-stabilization lets the system recover autonomously from an arbitrary system state, making the system recover from errors and temporarily broken assumptions. Clustering nodes within ad-hoc networks can help forming backbones, facilitating routing, improving scaling, aggregating information, saving power and much more. We present a self-stabilizing distributed (k,r)-clustering algorithm. A (k,r)-clustering assigns k cluster heads within r communication hops for all nodes in the network while trying to minimize the total number of cluster heads. The algorithm assumes a bound on clock frequency differences and a limited guarantee on message delivery. It uses multiple paths to different cluster heads for improved security, availability and fault tolerance. The algorithm assigns, when possible, at least k cluster heads to each node within O(rπλ3) time from an arbitrary system configuration, where π is a limit on message loss and λ is a limit on pulse rate differences. The set of cluster heads stabilizes, with high probability, to a local minimum within O(rπλ4glogn) time, where n is the size of the network and g is an upper bound on the number of nodes within 2r hops.