Parallel composition of stabilizing algorithms

Abstract

Worst case convergence time is primary measure of the complexity of a self-stabilizing algorithm. This aspect of complexity is not only theoretically interesting, but can be a practical limitation to stabilization's applicability in system design. Recently, a number of papers concentrated on conditional improvements in convergence time. Plausible conditions include rapid convergence for the most likely faulty initial states and accelerated convergence with respect to critical components of the global state, such as output variables. A general technique for speedup, used in many areas of computer science, is to exploit parallelism in the design of algorithms. The paper considers the explicit use of parallelism for self stabilization. A paradigm for composition based on parallel execution of several algorithms and an observer is proposed. Applications of parallel composition are shown in previously published research and for a new algorithm that is time adaptively stabilizing. Layered composition is, at present, a standard technique for designing stabilizing systems. The results of the paper go beyond the possibility of constructing stabilizing systems; attention is given to the issue of output convergence time in the compositional structure of the algorithm.