A Self-stabilizing (k,r)-clustering Algorithm with Multiple Paths for Wireless Ad-hoc Networks

Wireless Ad-hoc networks are distributed systems that often reside in error-prone environments. Self-stabilization lets the system recover autonomously from an arbitrary 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 the first 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 uses synchronous communication rounds and 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(r) rounds from an arbitrary configuration. The set of cluster heads stabilizes, with high probability, to a local minimum within O(gr log n) rounds, where n is the size of the network and g is an upper bound on the number of nodes within 2r hops.