A Stabilizing Rendition of MST Construction

A self-stabilizing construction of the minimum-spanning forest of distributed network is described. The algorithm demonstrates that techniques of graph reduction and iteration can be employed in the context of stabilizing distributed programs. The program development follows the principle of layering in the construction of self-stabilizing algorithms, where each layer corresponds to one level of iteration. The result is a relatively terminating program that can either be executed asynchronously or by using a stabilizing synchronizer. This paper presents a (self-) stabilizing algorithm to construct the minimum-weight spanning forest, MSF, of a network in which processes correspond to vertices and undirected edges designate allowable communication between processes. An algorithm is stabilizing if it speciies no precondition on its variables or program counter(s), yet is guaranteed to converge to a legitimate behaviour in nite time. Thus, in the case of constructing a MSF, the program's variables may initially have arbitrary values, yet after a nite computation, some subset of those variables will describe a minimum-weight spanning forest of the network. There are two standard interpretations of the application of the stabilizing property. First, consider application to fault-tolerance. A stabilizing algorithm overcomes arbitrary transient faults that may temporarily disrupt computation and set variables to unknown values: we regard the state following a temporary disruption as a new initial state (although there is no \initialization signal" to the program); once computation is again correct, then after a nite time the MSF is determined. Second, consider application to adaptive response in a dynamic network. A stabilizing algorithm reacts to (asynchronous) 0