  To get estimators that work within a certain error bound with high
probability, a common strategy is to design one that works with constant
probability, and then boost the probability using independent repetitions.
Important examples of this approach are small space algorithms for estimating
the number of distinct elements in a stream, or estimating the set similarity
between large sets. Using standard strongly universal hashing to process each
element, we get a sketch based estimator where the probability of a too large
error is, say, 1/4. By performing $r$ independent repetitions and taking the
median of the estimators, the error probability falls exponentially in $r$.
However, running $r$ independent experiments increases the processing time by a
factor $r$.
  Here we make the point that if we have a hash function with strong
concentration bounds, then we get the same high probability bounds without any
need for repetitions. Instead of $r$ independent sketches, we have a single
sketch that is $r$ times bigger, so the total space is the same. However, we
only apply a single hash function, so we save a factor $r$ in time, and the
overall algorithms just get simpler.
  Fast practical hash functions with strong concentration bounds were recently
proposed by Aamand em et al. (to appear in STOC 2020). Using their hashing
schemes, the algorithms thus become very fast and practical, suitable for
online processing of high volume data streams.
