Self-Stabilizing Master-Slave Token Circulation Algorithm in Undirected Rings and Unicyclic Graphs of Arbitrary Size and Their Orientations

Abstract

Token circulation is a fundamental task in the distributed systems. In this paper, we propose a constant space randomized self-stabilizing master-slave token circulation algorithm that works for undirected rings and undirected unicyclic graphs 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 (or unicyclic graph) of size n under an unfair distributed daemon; the nodes do not need the knowledge of the size of the ring and hence the protocol is suited for dynamic graphs. The proposed token circulation algorithm is further extended to achieve orientation in the ring and the unicyclic graph. Disregarding the time for stabilization, the orientation can be done in at most O(n) steps with 1 bit extra storage at each node for the ring and the unicyclic graph.