PageRank Computation Using a Multiple Implicitly Restarted Arnoldi Method for Modeling Epidemic Spread


A parallel implementation based on implicitly restarted Arnoldi method (MIRAM) is proposed for calculating dominant eigenpair of stochastic matrices derived from very large real networks. Their high damping factor makes many existing algorithms less efficient, while MIRAM could be promising. Also, we apply this method in an epidemic application. We describe in this paper a stochastic model based on PageRank to simulate the epidemic spread, where a PageRank-like infection vector is calculated by MIRAM to help establish efficient vaccination strategy. MIRAM is implemented within the framework of Trilinos, targeting big data and sparse matrices representing scale-free networks, also known as power law networks. Hypergraph partitioning approach is employed to minimize the communication overhead. The algorithm is tested on a nation wide cluster of clusters Grid5000. Experiments on very large networks such as twitter and yahoo with over 1 billion nodes are conducted. With our parallel implementation, a speedup of \(27\times \) is met compared to the sequential solver.

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We would like to thank Fabrcio Benevenuto from Federal University of Ouro Preto for the \(twitter\) network, Kim Capps from Yahoo! Labs for his help to get access to Alta Vista web network.

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Correspondence to Zifan Liu.

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Liu, Z., Emad, N., Amor, S.B. et al. PageRank Computation Using a Multiple Implicitly Restarted Arnoldi Method for Modeling Epidemic Spread. Int J Parallel Prog 43, 1028–1053 (2015).

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  • Epidemic
  • PageRank
  • Scale free networks
  • Power law
  • IRAM
  • Big data
  • Hypergraph partitioning