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184
The Glauber dynamics for colourings of bounded degree trees
, 2008
"... We study the Glauber dynamics Markov chain for kcolourings of trees with maximum degree ∆. For k ≥ 3, we show that the mixing time on every tree is at most n O(1+∆/(k log ∆)). This bound is tight up to the constant factor in the exponent, as evidenced by the complete tree. Our proof uses a weighted ..."
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Cited by 3 (0 self)
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We study the Glauber dynamics Markov chain for kcolourings of trees with maximum degree ∆. For k ≥ 3, we show that the mixing time on every tree is at most n O(1+∆/(k log ∆)). This bound is tight up to the constant factor in the exponent, as evidenced by the complete tree. Our proof uses a
The Mixing Time of Glauber Dynamics for Colouring Regular Trees
"... We consider Metropolis Glauber dynamics for sampling proper qcolourings of the nvertex complete bary tree when 3 ≤ q ≤ b/2 ln(b). We give both upper and lower bounds on the mixing time. For fixed q and b, our upper bound is n O(b / log b) and our lower bound is n Ω(b/q log(b)) , where the constan ..."
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Cited by 3 (0 self)
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We consider Metropolis Glauber dynamics for sampling proper qcolourings of the nvertex complete bary tree when 3 ≤ q ≤ b/2 ln(b). We give both upper and lower bounds on the mixing time. For fixed q and b, our upper bound is n O(b / log b) and our lower bound is n Ω(b/q log(b)) , where
Very rapid mixing of the Glauber dynamics for proper colourings on boundeddegree graphs
, 2000
"... Recent results have shown that the Glauber dynamics for graph colourings has optimal mixing time when (i) the graph is trianglefree and Dregular and the number of colours k is a small constant fraction smaller than 2D, or (ii) the graph has maximum degree D and k = 2D. We extend both these results ..."
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Cited by 10 (2 self)
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Recent results have shown that the Glauber dynamics for graph colourings has optimal mixing time when (i) the graph is trianglefree and Dregular and the number of colours k is a small constant fraction smaller than 2D, or (ii) the graph has maximum degree D and k = 2D. We extend both
Glauber Dynamics on Trees and Hyperbolic Graphs
, 2008
"... We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded degree. We ..."
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Cited by 8 (0 self)
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We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded degree. We
Glauber Dynamics on Trees and Hyperbolic Graphs
, 2001
"... We study discrete time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded degree. We show that the relaxation time (defined as the reciprocal of the spectral gap 1 \Gamma 2 ) for the dynami ..."
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Cited by 25 (9 self)
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We study discrete time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded degree. We show that the relaxation time (defined as the reciprocal of the spectral gap 1 \Gamma 2
ZIGZAG: An efficient peertopeer scheme for media streaming
 IN PROC. OF IEEE INFOCOM
, 2003
"... We design a peertopeer technique called ZIGZAG for singlesource media streaming. ZIGZAG allows the media server to distribute content to many clients by organizing them into an appropriate tree rooted at the server. This applicationlayer multicast tree has a height logarithmic with the number o ..."
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Cited by 279 (5 self)
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of clients and a node degree bounded by a constant. This helps reduce the number of processing hops on the delivery path to a client while avoiding network bottleneck. Consequently, the endtoend delay is kept small. Although one could build a tree satisfying such properties easily, an efficient control
Glauber dynamics on trees: boundary conditions and mixing time
 Comm. Math. Phys
"... We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics in the socalled Bethe approximation. Specifically, we show that spectral gap and the logSobolev constant of the Glauber dynamics for the Ising model on an nvertex regular tree ..."
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Cited by 30 (10 self)
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We give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the Glauber dynamics in the socalled Bethe approximation. Specifically, we show that spectral gap and the logSobolev constant of the Glauber dynamics for the Ising model on an nvertex regular tree
The Glauber dynamics on colourings of a graph with high girth and maximum degree
 In Proc. of the 34th ACM Symposium on Theory of Computing (STOC
, 2001
"... We prove that the Glauber dynamics on the C colourings of a graph G on n vertices with girth g and maximum degree mixes rapidly if (i) C = q and q > q where q = 1:4890::: is the root of = 1; and (ii) D log n and g D log for some constant D = D(q). This improves the corresponding ..."
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Cited by 2 (0 self)
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We prove that the Glauber dynamics on the C colourings of a graph G on n vertices with girth g and maximum degree mixes rapidly if (i) C = q and q > q where q = 1:4890::: is the root of = 1; and (ii) D log n and g D log for some constant D = D(q). This improves
Results 1  10
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184