Self-Stabilization by Local Checking and Correction

A self-stabilizing protocol is one that begins to behave correctly in bounded time, no matter what state the protocol is started in. Self-stabilization abstracts the ability of a protocol to tolerate arbitrary faults that stop. We investigate the power and applicability of local checking and correction for the design of stabilizing network protocols. A link subsystem is a pair of neighboring nodes and the two links between them. Intuitively, a protocol P is locally checkable if whenever P is in a bad state, some link subsystem is also in a bad state. A protocol P is locally correctable if P can be corrected to a good state by locally correcting link subsystems. We present four general techniques for designing stabilizing protocols. We rst show that every locally checkable and correctable protocol can be stabilized in time proportional to the height of an underlying partial order. Second, we show that every locally checkable protocol on a tree can be stabilized in time proportional to the height of the tree. Third, we show that every locally checkable protocol can be stabilized in time proportional to the number of network nodes. The third result shows that we can dispense with the need for local correctability or the need for the underlying topology to be a tree as long as we are willing to pay a higher price in stabilization time. Fourth, we show that any deterministic synchronous protocol can be converted to an asynchronous, stabilizing version of . The fourth technique is useful because there are network tasks for which a synchronous protocol exists but for which no asynchronous, locally checkable solution is known. We also present two useful heuristics. The rst heuristic, that of removing unexpected packet transitions, can often be used to transform a protocol into a locally checkable equivalent. A number of existing protocols work in a dynamic network model where links can fail and recover. The second heuristic states that locally checkable protocols for dynamic networks can sometimes be made locally correctable. The basic idea is to use the link failure and recovery actions of the original protocol to locally correct link subsystems. Together our techniques cover a broad range of networking tasks. We use our general techniques to construct new or improved stabilizing solutions to many speci c for Mutual Exclusion, Network Resets, Spanning Trees, Topology Update, Min Cost Flows etc. Many of our solutions are practical and can be applied to real networks without appreciable loss in e ciency. For example, the messages required for local checking can easily be piggybacked on the "keep-alive" tra c sent between neighbors in real networks. Our techniques also help in succinctly understanding existing stabilizing protocols. We