bhi5hmaraj / masters-thesis

My masters thesis at CMI on Random Spanning Trees

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