Conside; now the number of sets checked in the
second pass by Algorithm 2, in the case of a failure.
The collection S can, in principle, grow much. Each
independent miss can in the worst case generate as
many new candidates as there are frequent sets. Note,
however, that if the probability that a given set is a
miss is at most 6, then the probability of 1 independent
misses can be at most S’. In a pathological case the
misses are very much dependent: there is a very large
frequent set X such that its subsets only occur with
the whole X. If X is not frequent in a sample, then
also all its subsets are missed. At least in the application
domain of supermarket basket data this kind of
sets are very unlikely to exist at all.