  Set synchronization is a fundamental task in distributed applications and
implementations. Existing methods that synchronize simple sets are mainly based
on compact data structures such as Bloom filter and its variants. However,
these methods are infeasible to synchronize a pair of multisets which allow an
element to appear for multiple times. To this end, in this paper, we propose to
leverage the counting cuckoo filter (CCF), a novel variant of cuckoo filter, to
represent and thereafter synchronize a pair of multisets. The cuckoo filter
(CF) is a minimized hash table that uses cuckoo hashing to resolve collisions.
CF has an array of buckets, each of which has multiple slots to store element
fingerprints. Based on CF, CCF extends each slot as two fields, the fingerprint
field and the counter field. The fingerprint field records the fingerprint of
element which is stored by this slot; while the counter field counts the
multiplicity of the stored element. With such a design, CCF is competent to
represent any multiset. After generating and exchanging the respective CCFs
which represent the local multi-sets, we propose the query-based and the
decoding-based methods to identify the different elements between the given
multisets. The comprehensive evaluation results indicate that CCF outperforms
the counting Bloom filter (CBF) when they are used to synchronize multisets, in
terms of both synchronization accuracy and the space-efficiency, at the cost of
a little higher time-consumption.
