Set reconciliation with nearly optimal communication complexity

We consider the problem of efficiently reconciling two similar sets held by different hosts while minimizing the communication complexity. This type of problem arises naturally from gossip protocols used for the distribution of information, but has other applications as well. We describe an approach to such reconciliation based on the encoding of sets as polynomials. The resulting protocols exhibit tractable computational complexity and nearly optimal communication complexity. Moreover, these protocols can be adapted to work over a broadcast channel, allowing many clients to reconcile with one host based on a single broadcast