Reconciling Graphs and Sets of Sets

TL;DR

This paper introduces algorithms for reconciling sets of sets, with applications to graphs, databases, and documents, addressing differences efficiently in complex data structures.

Contribution

It generalizes set reconciliation to sets of sets, providing new algorithms and protocols for graph and tree reconciliation scenarios.

Findings

Protocols for random graphs from G(n,p)

Methods for reconciling forests of rooted trees

Efficient handling of differences in complex data structures

Abstract

We explore a generalization of set reconciliation, where the goal is to reconcile sets of sets. Alice and Bob each have a parent set consisting of $s$ child sets, each containing at most $h$ elements from a universe of size $u$. They want to reconcile their sets of sets in a scenario where the total number of differences between all of their child sets (under the minimum difference matching between their child sets) is $d$. We give several algorithms for this problem, and discuss applications to reconciliation problems on graphs, databases, and collections of documents. We specifically focus on graph reconciliation, providing protocols based on set of sets reconciliation for random graphs from $G(n,p)$ and for forests of rooted trees.