A self-stabilizing algorithm which finds a 2-center of a tree

In this paper, we design a self-stabilizing algorithm which finds a 2-center for a distributed system with a tree topology. Our algorithm is based on the algorithm in [1–3]. The latter enables us to find the center (or centers) for the tree. If we sever the tree at the center (or centers), we obtain two subtrees. One of the major works in this paper is to show that if we pick a center from each subtree, the two picked centers will constitute a 2-center for the original tree. With this in mind, we design our algorithm so that it is equipped with the ability of “sensing” the two subtrees and then finding a center in each of them.