Subset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width

نویسندگان

  • Magnus Bordewich
  • Ross J. Kang
چکیده

Motivated by the ‘subgraphs world’ view of the ferromagnetic Ising model, we analyse the mixing times of Glauber dynamics based on subset expansion expressions for classes of graph, hypergraph and matroid polynomials. With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs, hypergraphs and matroids of bounded tree-width. This extends known results on rapid mixing for the Tutte polynomial, adjacencyrank (R2-)polynomial and interlace polynomial. In particular Glauber dynamics for the R2-polynomial was known to mix rapidly on trees, which led to hope of rapid mixing on a wider class of graphs. We show that Glauber dynamics for a very wide class of polynomials mixes rapidly on graphs of bounded tree-width, including many cases in which the Glauber dynamics does not mix rapidly for all graphs. This demonstrates that rapid mixing on trees or bounded tree-width graphs does not offer strong evidence towards rapid mixing on all graphs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

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

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...

متن کامل

Branch-Width and Well-Quasi-Ordering in Matroids and Graphs

We prove that a class of matroids representable over a fixed finite field and with bounded branch-width is well-quasi-ordered under taking minors. With some extra work, the result implies Robertson and Seymour’s result that graphs with bounded tree-width (or equivalently, bounded branch-width) are well-quasi-ordered under taking minors. We will not only derive their result from our result on ma...

متن کامل

Rank-width and Well-quasi-ordering of Skew-Symmetric or Symmetric Matrices (extended abstract)

We prove that every infinite sequence of skew-symmetric or symmetric matrices M1, M2, . . . over a fixed finite field must have a pair Mi, Mj (i < j) such that Mi is isomorphic to a principal submatrix of the Schur complement of a nonsingular principal submatrix in Mj , if those matrices have bounded rank-width. This generalizes three theorems on well-quasi-ordering of graphs or matroids admitt...

متن کامل

Minor-matching hypertree width

In this paper we present a new width measure for a tree decomposition, minor-matching hypertree width, μ-tw, for graphs and hypergraphs, such that bounding the width guarantees that set of maximal independent sets has a polynomially-sized restriction to each decomposition bag. The relaxed conditions of the decomposition allow a much wider class of graphs and hypergraphs of bounded width compare...

متن کامل

Branch-Width, Parse Trees, and Monadic Second-Order Logic for Matroids

We introduce “matroid parse trees” which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounded branch-width over a finite field. We prove that if M is a family of matroids described by a sentence in the monadic second-order logic of matroids, then there is a finite tree automaton accepting exactly those parse trees which build v...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Electr. J. Comb.

دوره 21  شماره 

صفحات  -

تاریخ انتشار 2014