On the Performance of Dijkstra's Third Self-stabilizing Algorithm for Mutual Exclusion

In [Dij74] Dijkstra introduced the notion of self-stabilizing algorithms, and presented three such algorithms for the problem of mutual exclusion on a ring of processors. The third algorithm is the most interesting of these three, but is rather non intuitive. In [Dij86] a proof of its correctness was presented, but the question of determining its worst case complexity — that is, providing an upper bound on the number of moves of this algorithm until it stabilizes — remained open. In this paper we solve this question, and prove an upper bound of O(n2 ) (n being the size of the ring) for this algorithm’s complexity. This complexity applies to a centralized as well as to a distributed scheduler.

• Type: Conference
• Year: 2007
• Where: SSS
• Authors: Viacheslav Chernoy, Mordechai Shalom, Shmuel Zaks
• Keywords: Algorithm, Self-stabilizing Algorithms, SSS 2007, Upper Bound