Self-stabilizing overlay networks

Today's distributed systems exist on a scale that was unimaginable only a few decades ago. Distributed systems now can consist of thousands or even millions of computers spread across the entire world. These large systems are often organized into overlay networks - networks composed of virtual links, with each virtual link realized by one or more physical links. Self-stabilizing overlay networks promise that, starting from any weakly-connected configuration, the correct network topology is always built. This area of research is young, and prior examples of self-stabilizing overlay networks have either been for simple topologies, or involved complex algorithms that were difficult to verify and extend. We address these limitations in this thesis.

First, we present the Transitive Closure Framework, a generic framework to transform any locally-checkable overlay network into a self-stabilizing network. This simple framework has a running time which is at most a logarithmic number of rounds more than optimal, and in fact is optimal for a particular class of overlay networks. We also prove the only known non-trivial lower bound on the convergence time of any self-stabilizing overlay network. To allow fast and efficient repairs for local faults, we extend the Transitive Closure Framework to the Local Repair Framework. We demonstrate this framework by implementing an efficient algorithm for node joins in the Skip+ graph.

Next, we present the Avatar network, which is a generic locally checkable overlay network capable of simulating many other overlay networks. We design a self-stabilizing algorithm for a binary search tree embedded onto the Avatar network, and prove this algorithm requires only a polylogarithmic number of rounds to converge and limits degree increases to within a polylogarithmic factor of optimal. This algorithm is the first to achieve such efficiency, and its modular design makes it easy to extend. Finally, we introduce a technique called network scaffolding, which builds other overlay network topologies using the Avatar network.