A Nearly Optimal Upper Bound for the Self-Stabilization Time in Herman's
In Distributed Computing
, 28: 233-244, 2015.Downloads: pdf, bibURL: http://dx.doi.org/10.1007/s00446-015-0241-z
Abstract. Self-stabilization algorithms are very important in designing fault-tolerant distributed systems. In this paper we consider Herman's self-stabilization algorithm and study its expected termination time. McIver and Morgan have conjectured the optimal upper bound being 0.148N^2, where N denotes the number of processors. We present an elementary proof showing a bound of 0.167N^2, a sharp improvement compared with the best known bound 0.521N^2. Our proof is inspired by McIver and Morgan's approach: we find a nearly optimal closed form of the expected stabilization time for any initial configuration, and apply the Lagrange multipliers method to give an upper bound.