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

TL;DR

This paper introduces the first space-efficient fully-dynamic dictionary and filter that support insertions, deletions, and queries with a constant number of memory accesses in the worst case, improving efficiency for dynamic set management.

Contribution

It presents novel designs for a fully-dynamic dictionary and filter that operate with constant memory access, supporting multisets and achieving high probability guarantees.

Findings

Supports insertions, deletions, and queries with constant memory accesses

Achieves space efficiency comparable to previous static structures

First in-memory fully-dynamic filter with proven properties

Abstract

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.