4 research outputs found
Multi-Party Set Reconciliation Using Characteristic Polynomials
In the standard set reconciliation problem, there are two parties and
, each respectively holding a set of elements and . The goal is
for both parties to obtain the union . In many distributed
computing settings the sets may be large but the set difference
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.Comment: 6 page
Reconciling Graphs and Sets of Sets
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
child sets, each containing at most elements from a universe of size .
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 . 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 and for forests of rooted trees