Tree algorithms for set reconciliation

Abstract: In this work, a set reconciliation setting is considered in which two parties have similar sets that they would like to reconcile. In particular, we focus on a divide-and-conquer strategy known as partitioned set reconciliation (PSR), in which the sets to be reconciled are successively partitioned until they contain a number of differences below some predetermined value. Borrowing techniques from tree-algorithms for random-access protocols, we present and analyze a novel set reconciliation scheme that we term enhanced partitioned set reconciliation (EPSR). This approach improves the efficiency in terms of overhead, i.e., it yields a lower communication cost, while keeping the same time and communication round complexity as PSR. Additionally, we simulate the performance of the proposed algorithm in an event-driven simulator. Our findings indicate that this novel protocol nearly halves the communication cost of PSR while maintaining the same time complexity.