  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.
