An Efficient and Scalable Algorithm for Estimating Kemeny's Constant of a Markov Chain on Large Graphs

Shiju Li, Xin Huang, Chul-Ho Lee

Abstract: The mean hitting time of a Markov chain on a graph from an arbitrary node to a target node randomly chosen according to its stationary distribution is called Kemeny's constant, which is an important metric for network analysis and has a wide range of applications. It is, however, still computationally expensive to evaluate the Kemeny's constant, especially when it comes to a large graph, since it requires the computation of the spectrum of the corresponding transition matrix or its normalized Laplacian matrix. In this paper, we propose a simple yet computationally efficient Monte Carlo algorithm to approximate the Kemeny's constant, which is equipped with an ε,δ)-approximation estimator. Thanks to its inherent algorithmic parallelism, we are able to develop its parallel implementation on a GPU to speed up the computation. We provide extensive experiment results on 13 real-world graphs to demonstrate the computational efficiency and scalability of our algorithm, which achieves up to 500x speed-up over the state-of-the-art algorithm. We further present its practical enhancements to make our algorithm ready for practical use in real-world settings.