Self-Stabilizing Master-Slave Token Circulation Algorithm in an Undirected Ring of Arbitrary Size and Its Orientation

Token circulation is a fundamental task in the distributed systems. In this paper, we propose a constant space self-stabilizing master-slave token circulation algorithm for an undirected ring of arbitrary size. We consider the recently introduced and studied master-slave model where a single node is designated to be a master node and other nodes are anonymous slave nodes. The expected stabilization time is O(n log n) steps, and the space requirement at each node is 4 bits for any undirected ring of size n; the nodes do not need the knowledge of the size of the ring and hence the protocol is suited for dynamic rings. The proposed token circulation algorithm is further extended to achieve ring orientation. Disregarding the time for stabilization, the ring orientation can be done in at most 3n - 1 steps with 1 bit extra storage at each node.