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The Relative Complexity of Approximate Counting Problems


Two natural classes of counting problems that are interreducible under approximation-preserving reductions are: (i) those that admit a particular kind of efficient approximation algorithm known as an “FPRAS”, and (ii) those that are complete for #P with respect to approximation-preserving reducibility. We describe and investigate not only these two classes but also a third class, of intermediate complexity, that is not known to be identical to (i) or (ii). The third class can be characterised as the hardest problems in a logically defined subclass of #P.

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Correspondence to Martin Dyer, Leslie Ann Goldberg, Catherine Greenhill or Mark Jerrum.

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Dyer, M., Goldberg, L., Greenhill, C. et al. The Relative Complexity of Approximate Counting Problems. Algorithmica 38, 471–500 (2004).

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  • Approximate counting
  • Computational complexity