A new parallel algorithm for solving large-scale Markov chains

Abderezak Touzene*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)239-253
Number of pages15
JournalJournal of Supercomputing
Issue number1
Publication statusPublished - Jan 2014


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

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Information Systems
  • Hardware and Architecture


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