Red Light Green Light Method for Solving Large Markov Chains

نویسندگان

چکیده

Discrete-time discrete-state finite Markov chains are versatile mathematical models for a wide range of real-life stochastic processes. One most common tasks in studies is computation the stationary distribution. Without loss generality, and drawing our motivation from applications to large networks, we interpret this problem as one computing distribution random walk on graph. We propose new controlled, easily distributed algorithm task, briefly summarized follows: at beginning, each node receives fixed amount cash (positive or negative), iteration, some nodes receive `green light' distribute their wealth debt proportionally transition probabilities chain; probability computed ratio by total all together. Our method includes special cases known, very different, previously disconnected methods including power iterations, Gauss-Southwell, online algorithms. prove exponential convergence method, demonstrate its high efficiency, derive scheduling strategies green-light, that achieve rate faster than state-of-the-art

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ژورنال

عنوان ژورنال: Journal of Scientific Computing

سال: 2022

ISSN: ['1573-7691', '0885-7474']

DOI: https://doi.org/10.1007/s10915-022-01976-8