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We present an improved "cooling schedule" for simulated annealing algorithms for combinatorial counting problems. Under our new schedule the rate of cooling accelerates as the temperature decreases. Thus, fewer intermediate temperatures are needed as the simulated annealing algorithm moves from the high temperature (easy region) to the low temperature(More)
We consider the problem of sampling independent sets of a graph with maximum degree. The weight of each independent set is expressed in terms of a xed positive parameter 2 ?2 , where the weight of an independent set is jj. The Glauber dynamics is a simple Markov chain Monte Carlo method for sampling from this distribution. We show fast convergence of this(More)
We analyze Markov chains for generating a random k-coloring of a random graph Gn,d/n. When the average degree d is constant, a random graph has maximum degree log n/ log log n, with high probability. We efficiently generate a random k-coloring when k = Ω(log log n/ log log log n), i.e., with many fewer colors than the maximum degree. Previous results hold(More)
We study two widely used algorithms, Glauber dynamics and the Swendsen-Wang algorithm, on rectangular subsets of the hypercubic lattice Z. We prove that under certain circumstances, the mixing time in a box of side length L with periodic boundary conditions can be exponential in L. In other words, under these circumstances, the mixing in these widely used(More)
This note considers the problem of sampling from the set of weighted independent sets of a graph with maximum degree ∆. For a positive fugacity λ, the weight of an independent set σ is λ|σ|. Luby and Vigoda proved that the Glauber dynamics, which only changes the configuration at a randomly chosen vertex in each step, has mixing time O(n log n) when λ < 2(More)
We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the stationary distribution to avoid worst-case configurations which arise in the traditional approach.As an application, we show(More)
We present a new technique for constructing and analyzing couplings to bound the convergence rate of finite Markov chains. Our main theorem is a generalization of the path coupling theorem of Bubley and Dyer, allowing the defining partial couplings to have length determined by a random stopping time. Unlike the original path coupling theorem, our version(More)