Research Report CS-RR-370
Martin Dyer, Leslie Ann Goldberg, Catherine Greenhill and Mark Jerrum, On the Relative Complexity of Approximate Counting Problems (February 20, 2000).
Abstract
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.