Rapid Mixing of Subset Glauber Dynamics on Graphs of Bounded Tree-Width

  • Magnus Bordewich
  • Ross J. Kang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)


Motivated by the ‘subgraphs world’ view of the ferromagnetic Ising model, we develop a general approach to studying mixing times of Glauber dynamics based on subset expansion expressions for a class of graph polynomials. With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs of bounded tree-width. This extends known results on rapid mixing for the Tutte polynomial, the adjacency-rank (R 2-)polynomial and the interlace polynomial.


Markov chain Monte Carlo graph polynomials subset expansion tree-width canonical paths randomised approximation schemes rapid mixing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Magnus Bordewich
    • 1
  • Ross J. Kang
    • 1
  1. 1.Durham UniversityDurhamUK

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