  Many applications of approximate membership query data structures, or
filters, require only an incremental filter that supports insertions but not
deletions. However, the design space of incremental filters is missing a "sweet
spot" filter that combines space efficiency, fast queries, and fast insertions.
Incremental filters, such as the Bloom and blocked Bloom filter, are not space
efficient. Dynamic filters (i.e., supporting deletions), such as the cuckoo or
vector quotient filter, are space efficient but do not exhibit consistently
fast insertions and queries.
  In this paper, we propose the prefix filter, an incremental filter that
addresses the above challenge: (1) its space (in bits) is similar to
state-of-the-art dynamic filters; (2) query throughput is high and is
comparable to that of the cuckoo filter; and (3) insert throughput is high with
overall build times faster than those of the vector quotient filter and cuckoo
filter by $1.39\times$-$1.46\times$ and $3.2\times$-$3.5\times$, respectively.
We present a rigorous analysis of the prefix filter that holds also for
practical set sizes (i.e., $n=2^{25}$). The analysis deals with the probability
of failure, false positive rate, and probability that an operation requires
accessing more than a single cache line.
