Constant Space Self-Stabilizing Center Finding in Anonymous Tree Networks
It is known that there is no self-stabilizing silent distributed algorithm for finding the center (or centers) of an anonymous tree network that uses less than O(log diam) space per process, where diam is the diameter of the tree. In this paper, a self-stabilizing, but non-silent, distributed algorithm, STC, for this problem is given, which takes O(diam) rounds under the unfair daemon and uses O(1) space per process. The method is to first construct a silent O(1)-space algorithm for the problem that works under the synchronous daemon, provided it has a clean start. A transformer is then constructed, which transforms any tree algorithm which is silent under the synchronous algorithm given a clean start into an equivalent non-silent self-stabilizing algorithm with the same asymptotic space complexity. The desired center finding algorithm, CSTC, is then obtained by applying the transformer to STC.