We consider a set reconciliation setting in which two parties hold similar sets which they would like to reconcile In particular, we focus on set reconciliation based on invertible Bloom lookup tables (IBLTs), a probabilistic data structure inspired by Bloom filters but allowing for more complex operations. IBLT-based set reconciliation schemes have the advantage of exhibiting a low complexity, however, the schemes available in literature are known to be far from optimal in terms of communication complexity (overhead). The inefficiency of IBLT-based set reconciliation can be attributed to two facts. First, it requires an estimate of the cardinality of the set difference between the sets, which implies an increase in overhead. Second, in order to cope with errors in the aforementioned estimation of the cardinality of the set difference, IBLT schemes in literature make a worst-case assumption and oversize the data structures, thus further increasing the overhead. In this work, we present a novel IBLT-based set reconciliation protocol that does not require estimating the cardinality of the set difference. The scheme we propose relies on what we term multi-edge-type (MET) IBLTs. The simulation results shown in this paper show that the novel scheme outperforms previous IBLT-based approaches to set reconciliation

翻译：我们考虑一个集合调和场景：两方持有相似的集合，并希望对其进行调和。具体而言，我们聚焦于基于可逆布隆查找表（IBLT）的集合调和方案。IBLT是一种受布隆过滤器启发但支持更复杂操作的概率性数据结构。基于IBLT的集合调和方案具有低复杂度的优势，然而现有文献中的方案在通信复杂度（开销）方面远未达到最优。这种低效性可归因于两个事实：首先，它需要估计集合差集基数，这会导致开销增加；其次，为应对前述差集基数估计中的误差，现有IBLT方案采用最坏情况假设并扩大数据结构规模，从而进一步增加开销。本文提出了一种新型基于IBLT的集合调和协议，该协议无需估计差集基数。我们提出的方案依赖于一种称为“多边类型”（MET）IBLT的结构。仿真结果表明，该新型方案在集合调和性能上优于先前基于IBLT的方法。