Red Light Green Light Method for Solving Large Markov Chains

Abstract

Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One of most common tasks in studies of Markov chains is computation of the stationary distribution. We propose a new general controlled, easily distributed algorithm for this task. The algorithm includes as special cases a wide range of known, very different, and previously disconnected methods including power iterations, versions of Gauss-Southwell formerly restricted to substochastic matrices, and online distributed algorithms. We prove exponential convergence of our method, demonstrate its high efficiency, and derive straightforward control strategies that achieve convergence rates faster than state-of-the-art algorithms.

Extreme Value Statistics for Evolving Random Networks

“…Let us assume again that s communities with the largest amount of nodes are taken and the ith community, 1 ≤ i ≤ s, contains m i nodes. Let method proposed in [147] demonstrates exponential convergence. However, the problem of the PageRank calculation is not the focus of the present survey.…”