A nearly optimal upper bound for the self-stabilization time in Hermans algorithm
Self-stabilization algorithms are very important in designing fault-tolerant distributed systems. In this paper we consider Hermans 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 Morgans 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.
self-stabilization hermans algorithm lagrange multipliers method