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FOCS
2007
IEEE

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

14 years 4 months ago
Adaptive Simulated Annealing: A Near-optimal Connection between Sampling and Counting
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 Z of a discrete system, such as the Ising model, matchings or colorings of a graph. The standard approach to estimating the partition function Z(β∗ ) at some desired inverse temperature β∗ is to define a sequence, which we call a cooling schedule, β0 = 0 < β1 < · · · < β = β∗ where Z(0) is trivial to compute and the ratios Z(βi+1)/Z(βi) are easy to estimate by sampling from the distribution corresponding to Z(βi). Previous approaches required a cooling schedule of length O∗ (ln A) where A = Z(0), thereby ensuring that each ratio Z(βi+1)/Z(βi) is bounded. We present a cooling schedule of length = O∗ ( √ ln A). For well-studied problems such as estimating the partition function of the Ising model, or approximating the number of co...
Daniel Stefankovic, Santosh Vempala, Eric Vigoda
Added 02 Jun 2010
Updated 02 Jun 2010
Type Conference
Year 2007
Where FOCS
Authors Daniel Stefankovic, Santosh Vempala, Eric Vigoda
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