  Invertible Bloom Filter (IBF) is a data structure, which employs a small set
of hash functions. An IBF allows for an efficient insertion and, with high
probability, for an efficient extraction of the data. However, the success
probability of the extraction depends on the storage overhead of an IBF and the
amount of the data stored. In an application, such as set reconciliation, where
there is a need to extract data stored in the IBF, the extraction might succeed
only partially, by recovering only part of the stored data. In this work, the
probability of success for a partial extraction of data from an IBF is
analyzed. It is shown that partial extraction could be useful in applications,
such as set reconciliation. In particular, it allows for set reconciliation by
using the IBF, where the storage overhead is too small to allow full
extraction. An upper bound on the number of rounds in an iterative set
reconciliation protocol is presented. The numerical results are derived
analytically, and confirmed by the computer simulations.
