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My masters thesis at CMI on Random Spanning Trees

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Random Spanning Trees

My masters thesis at CMI on Random Spanning Trees. The following this the approximate content of the thesis. A much more updated version is here . The template used is available here.

  • Intro

  • Background

    • Fundamental theorem of Markov Chains
    • Some basic Spectral Graph Theory
    • Kirchoff matrix tree theorem
    • Some basic facts about electric networks
  • The Random Walk Approach
    • Aldous, Broder **
      • Explain this in detail
    • Wilson
  • The Matrix Approach
    • CMN
    • CDN
    • Harvey, Xu ***
      • Explain this in detail
    • Kulkarni and Gunoche
  • The Laplacian Paradigm
    • KM09 and also mention the improvement

  • Applications, Conclusion and State of the Art

    • Expander Graphs
    • TSP approx algo
    • Random Spanning Trees for Expanders, Sparsifiers, and Virtual Network Security
    • A table which consolidates all the algorithms