Space optimal PIF algorithm: self-stabilized with no extra space

Recently (1998), we introduced a new self-stabilizing PIF paradigm, called the Propagation of information with Feedback and Cleaning (PFC), for the rooted tree networks. In this paper, we propose the first self-stabilizing PIF scheme for the tree networks without sense of direction-the trees do not have a root and the processors do not maintain any ancestor. The proposed PIF scheme is based on the paradigm PFC. A PIF algorithm in trees without sense of direction is very useful in many applications because this allows to maintain only one spanning tree of the network instead of one per processor. The proposed algorithm requires 3 states per processor, and only 2 states for the initiator and leaves. This space requirement is optimal for both self-stabilizing and non-stabilizing PIF algorithms on tree networks. Thus, the processors need no extra space to stabilize the proposed PIF scheme.