Bloom maps

TL;DR

This paper introduces Bloom maps, a new data structure for efficiently encoding static maps to support approximate queries, with proven bounds on space requirements related to error rate and value distribution entropy.

Contribution

The paper presents Bloom maps, a novel generalization of Bloom filters, along with tight upper and lower bounds on space complexity for approximate static map encoding.

Findings

Bloom maps efficiently encode static maps with controlled error.

Theoretical bounds on space requirements are established, differing by a factor of log e.

The data structure generalizes Bloom filters for approximate map queries.

Abstract

We consider the problem of succinctly encoding a static map to support approximate queries. We derive upper and lower bounds on the space requirements in terms of the error rate and the entropy of the distribution of values over keys: our bounds differ by a factor log e. For the upper bound we introduce a novel data structure, the Bloom map, generalising the Bloom filter to this problem. The lower bound follows from an information theoretic argument.