Empire of colonies: Self-stabilizing and self-organizing distributed algorithm

Abstract

Self-stabilization ensures automatic recovery from an arbitrary state; we define self-organization as a property of algorithms which display local attributes. More precisely, we say that an algorithm is self-organizing if (1) it converges in sublinear time and (2) reacts “fast” to topology changes. If s ( n ) is an upper bound on the convergence time and d ( n ) is an upper bound on the convergence time following a topology change, then s ( n ) ∈ o ( n ) and d ( n ) ∈ o ( s ( n ) ) . The self-organization property can then be used for gaining, in sub-linear time, global properties and reaction to changes. We present self-stabilizing and self-organizing algorithms for many distributed algorithms, including distributed snapshot and leader election. We present a new randomized self-stabilizing distributed algorithm for cluster definition in communication graphs of bounded degree processors. These graphs reflect sensor networks deployment. The algorithm converges in O ( log n ) expected number of rounds, handles dynamic changes locally and is, therefore, self-organizing. Applying the clustering algorithm to specific classes of communication graphs, in O ( log n ) levels, using an overlay network abstraction, results in a self-stabilizing and self-organizing distributed algorithm for hierarchy definition. Given the obtained hierarchy definition, we present an algorithm for hierarchical distributed snapshots. The algorithms are based on a new basic snap-stabilizing snapshot algorithm, designed for message passing systems in which a distributed spanning tree is defined and in which processors communicate using bounded links capacity. The algorithm is on-demand self-stabilizing when no such distributed spanning tree is defined. Namely, it stabilizes regardless of the number of snapshot invocations. The combination of the self-stabilizing and self-organizing distributed hierarchy construction and the snapshot algorithm forms an efficient self-stabilizer transformer. Given a distributed algorithm for a specific task, we are able to convert the algorithm into a self-stabilizing algorithm for the same task with an expected convergence time of O ( log 2 n ) rounds.