On The Complexity of Enumeration

We investigate the relationship between several enumeration complexity classes and focus in particular on the incremental polynomial time and the polynomial delay (IncP and DelayP). We prove, modulo the Exponential Time Hypothesis, that IncP contains a strict hierarchy of subclasses. Since DelayP is included in IncP1, the first class of the hierarchy, it is separated from IncP. We prove for some algorithms that we can turn an average delay into a worst case delay, suggesting that IncP1 = DelayP even with a polynomially bounded memory. Finally we relate the uniform generation of solutions to probabilistic enumeration algorithms with polynomial delay. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems