Robust Set Reconciliation via Locality Sensitive Hashing

TL;DR

This paper introduces a new method for robust set reconciliation in metric spaces using locality sensitive hashing and invertible Bloom lookup tables, improving scalability and efficiency in high-dimensional geometric settings.

Contribution

It presents a novel combination of locality sensitive hashing and invertible Bloom lookup tables for efficient, robust set reconciliation in geometric spaces, including a new variation of the problem.

Findings

Improved scalability with space dimension

Efficient communication in geometric settings

Novel approach for a new set reconciliation variation

Abstract

We consider variations of set reconciliation problems where two parties, Alice and Bob, each hold a set of points in a metric space, and the goal is for Bob to conclude with a set of points that is close to Alice's set of points in a well-defined way. This setting has been referred to as robust set reconciliation. More specifically, in one variation we examine the goal is for Bob to end with a set of points that is close to Alice's in earth mover's distance, and in another the goal is for Bob to have a point that is close to each of Alice's. The first problem has been studied before; our results scale better with the dimension of the space. The second problem appears new. Our primary novelty is utilizing Invertible Bloom Lookup Tables in combination with locality sensitive hashing. This combination allows us to cope with the geometric setting in a communication-efficient manner.