  We investigate the relationship between several enumeration complexity
classes and focus in particular on problems having enumeration algorithms with
incremental and polynomial delay (IncP and DelayP respectively). We show that,
for some algorithms, we can turn an average delay into a worst case delay
without increasing the space complexity, suggesting that IncP_1 = DelayP even
with polynomially bounded space. We use the Exponential Time Hypothesis to
exhibit a strict hierarchy inside IncP which gives the first separation of
DelayP and IncP. Finally we relate the uniform generation of solutions to
probabilistic enumeration algorithms with polynomial delay and polynomial
space.
