Journal
ALGORITHMICA
Volume 38, Issue 3, Pages 471-500Publisher
SPRINGER
DOI: 10.1007/s00453-003-1073-y
Keywords
approximate counting; computational complexity
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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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