Exact set reconciliation based on bloom filters

We explore the problem of reconciling two similar sets that were maintained by distributed nodes while minimizing communication cost and reconciliation latency. This problem has a wide variety of applications including gossip protocol, mobile database synchronization, distributed file system and maintenance of routing tables in the face of node failures. Existing solutions to exact reconciliation are based on characteristic polynomial interpolation, but their latency is too long. To reduce the latency of such algorithms, we presented an exact set reconciliation algorithm based on Bloom filters (BFESR). The basic idea of BFESR is to obtain symmetric difference size in advance, thus characteristic polynomial values are wholesale transferred. At first, BFESR estimates symmetric difference size using Bloom filters, and calculates multiple polynomial values according to estimated symmetric difference set, and then interpolates rational polynomials, finally recovers the union of sets through factoring the rational polynomials. Theoretical analyses and experimental results show that, compared with the existing methods for exact set reconciliation, BFESR needs only a single round-trip to get the accurate union of sets in most cases, thus greatly reducing reconciliation latency.