Multi-Party Set Reconciliation Using Characteristic Polynomials

TL;DR

This paper explores multi-party set reconciliation using characteristic polynomials, comparing their efficiency with Invertible Bloom Lookup Tables in distributed settings where set differences are small.

Contribution

It introduces the use of characteristic polynomials for multi-party set reconciliation and compares their performance to existing Invertible Bloom Lookup Table methods.

Findings

Characteristic polynomials offer an alternative approach for multi-party reconciliation.

Performance comparison shows trade-offs between polynomial and IBLT methods.

Potential for more efficient communication in distributed systems with small set differences.

Abstract

In the standard set reconciliation problem, there are two parties $A_1$ and $A_2$, each respectively holding a set of elements $S_1$ and $S_2$. The goal is for both parties to obtain the union $S_1 \cup S_2$. In many distributed computing settings the sets may be large but the set difference $|S_1-S_2|+|S_2-S_1|$ is small. In these cases one aims to achieve reconciliation efficiently in terms of communication; ideally, the communication should depend on the size of the set difference, and not on the size of the sets. Recent work has considered generalizations of the reconciliation problem to multi-party settings, using a framework based on a specific type of linear sketch called an Invertible Bloom Lookup Table. Here, we consider multi-party set reconciliation using the alternative framework of characteristic polynomials, which have previously been used for efficient pairwise set reconciliation protocols, and compare their performance with Invertible Bloom Lookup Tables for these problems.