Memory Adaptive Self-Stabilizing Protocols (Extended Abstract)

We present a token-based diffusion scheme that forms the basis of efficient self-stabilizing protocols for a variety of problems including unique naming, network topology, token management. For the model where processors’ initial knowledge about the network is restricted only to their neighbours, we introduce the concept of memory adaptive protocols. In these, once the system stabilizes, the size of the memory used by each processor is a function of the actual network size — even though the system may have been started in a state where each processor “thinks” that it is embedded in a network much larger (or smaller) than the actual one. For this model, we develop memory adaptive self-stabilizing protocols for the problems mentioned above that stabilize in time O(n log log n), where n is the number of processors. For the model where processors also know an upper bound D on the diameter of the network and an upper bound on n, we develop bounded-memory self-stabilizing protocols for the same problems that stabilize in O(min{D,n}) time. All our protocols are based on a token diffusion scheme, and are uniform, in the sense that processors with the same number of neighbours execute the same program.