Set-Difference Range Queries

TL;DR

This paper introduces set-difference range queries, a new problem involving symmetric differences between sets in geometric ranges, and proposes a framework using signed symmetric-difference sketches and invertible Bloom filters to efficiently solve them.

Contribution

The paper presents a novel framework for set-difference range queries utilizing signed symmetric-difference sketches and invertible Bloom filters, enabling efficient computation in various scenarios.

Findings

Framework based on signed symmetric-difference sketches is effective.

Invertible Bloom filters enable composition, differencing, and searching.

Applicable to a wide range of geometric query scenarios.

Abstract

We introduce the problem of performing set-difference range queries, where answers to queries are set-theoretic symmetric differences between sets of items in two geometric ranges. We describe a general framework for answering such queries based on a novel use of data-streaming sketches we call signed symmetric-difference sketches. We show that such sketches can be realized using invertible Bloom filters (IBFs), which can be composed, differenced, and searched so as to solve set-difference range queries in a wide range of scenarios.