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A new parallel algorithm for solving large-scale Markov chains

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Abstract

In this paper, we propose a new parallel sparse iterative method (PPSIA) for computing the stationary distribution of large-scale Markov chains. The PPSIA method is based on Markov chain state isolation and aggregation techniques. The parallel method conserves as much as possible the benefits of aggregation, and Gauss–Seidel effects contained in the sequential algorithm (SIA) using a pipelined technique. Both SIA and PPSIA exploit sparse matrix representation in order to solve large-scale Markov chains. Some Markov chains have been tested to compare the performance of SIA, PPSIA algorithms with other techniques such as the power method, and the generalized minimal residual GMRES method. In all the tested models, PPSIA outperforms the other methods and shows a super-linear speed-up.

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Acknowledgements

We thank Sultan Qaboos University for providing the High Performance Computer (HPC). We also thank Professor William Stewart for making the MARCA software available.

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Correspondence to Abderezak Touzene.

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Touzene, A. A new parallel algorithm for solving large-scale Markov chains. J Supercomput 67, 239–253 (2014). https://doi.org/10.1007/s11227-013-0997-5

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Keywords

  • Performance evaluation
  • Markov chains
  • Iterative methods
  • Aggregation techniques