On Clusters in Markov Chains

  • Nir Ailon
  • Steve Chien
  • Cynthia Dwork
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3887)


Motivated by the computational difficulty of analyzing very large Markov chains, we define a notion of clusters in (not necessarily reversible) Markov chains, and explore the possibility of analyzing a cluster “in vitro,” without regard to the remainder of the chain. We estimate the stationary probabilities of the states in the cluster using only transition information for these states, and bound the error of the estimate in terms of parameters measuring the quality of the cluster. Finally, we relate our results to searching in a hyperlinked environment, and provide supporting experimental results.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nir Ailon
    • 1
  • Steve Chien
    • 2
  • Cynthia Dwork
    • 2
  1. 1.Princeton UniversityPrincetonUSA
  2. 2.Microsoft ResearchMountain ViewUSA

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