Set reconciliation using rational polynomials

In various distributed systems, it may happen that parties need to find a union of their data sets. This may happen in database synchronisation, shared file systems and during the use of gossip protocols. Generic approaches have been using interactive protocols where they also share common records. This approach leads to communication complexity being dependant of the size of sets and is clearly inefficient if the sets are large but the differences are small. The problem can be defined as follows: given two hosts A and B, having sets SA and SB accordingly, how can we find the union S = SA ∪ SB with minimal communication complexity. That is, how to find union with minimal number of interactions and minimal amount of information transmitted. This problem is called set reconciliation problem. The problem has been studied in [3], [1], [7] and in other papers. To overcome the problem with transmitting information about shared records, researchers have used Reed-Solomon codes, colouring graphs and representing sets as characteristic polynomials. The latter method was also studied in [6], which is also the main article this report is based on.