Distance Sensitive Bloom Filters Without False Negatives

TL;DR

This paper introduces distance sensitive Bloom filters that avoid false negatives, providing tight bounds on space efficiency for set proximity queries in Hamming space, crucial for applications requiring high reliability.

Contribution

It presents the first false-negative-free distance sensitive Bloom filters with tight space bounds, advancing the reliability of proximity queries in high-dimensional data.

Findings

Established tight upper bounds on space for false-negative-free filters.

Derived lower bounds matching the upper bounds in several cases.

Demonstrated the feasibility of reliable proximity queries without false negatives.

Abstract

A Bloom filter is a widely used data-structure for representing a set $S$ and answering queries of the form "Is $x$ in $S$?". By allowing some false positive answers (saying "yes" when the answer is in fact `no') Bloom filters use space significantly below what is required for storing $S$. In the distance sensitive setting we work with a set $S$ of (Hamming) vectors and seek a data structure that offers a similar trade-off, but answers queries of the form "Is $x$ close to an element of $S$?" (in Hamming distance). Previous work on distance sensitive Bloom filters have accepted false positive and false negative answers. Absence of false negatives is of critical importance in many applications of Bloom filters, so it is natural to ask if this can be also achieved in the distance sensitive setting. Our main contributions are upper and lower bounds (that are tight in several cases) for space usage in the distance sensitive setting where false negatives are not allowed.