Adaptive Simulated Annealing: A Near-optimal Connection between Sampling and Counting

@article{Stefankovic2007AdaptiveSA,
  title={Adaptive Simulated Annealing: A Near-optimal Connection between Sampling and Counting},
  author={Daniel Stefankovic and Santosh Vempala and Eric Vigoda},
  journal={48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)},
  year={2007},
  pages={183-193}
}
We present a near-optimal reduction from approximately counting the cardinality of a discrete set to approximately sampling elements of the set. An important application of our work is to approximating the partition function <i>Z</i> of a discrete system, such as the Ising model, matchings or colorings of a graph. The typical approach to estimating the partition function <i>Z</i>(β<sup>*</sup>) at some desired inverse temperature β<sup>*</sup> is to define a sequence, which we call a <i>cooling… CONTINUE READING
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