Fully-Dynamic Space-Efficient Dictionaries and Filters with Constant Number of Memory Accesses

A fully-dynamic dictionary is a data structure for maintaining sets that supports insertions, deletions and membership queries. A filter approximates membership queries with a one-sided error. We present two designs:

1. The first space-efficient fully-dynamic dictionary that maintains both sets and random multisets and supports queries, insertions, and deletions with a constant number of memory accesses in the worst case with high probability. The comparable dictionary of Arbitman, Naor, and Segev [FOCS 2010] works only for sets.
2. By a reduction from our dictionary for random multisets, we obtain a space-efficient fully-dynamic filter that supports queries, insertions, and deletions with a constant number of memory accesses in the worst case with high probability (as long as the false positive probability is $2^{-O(w)}$, where $w$ denotes the word length). This is the first in-memory space-efficient fully-dynamic filter design that provably achieves these properties. We also present an application of the techniques used to design our dictionary to the static Retrieval Problem.