Cardinality Computing: A New Step Towards Fully Representing Multi-sets by Bloom Filters

Bloom Filters are space and time efficient randomized data structures for representing (multi-)sets with certain allowable errors, and are widely used in many applications. Previous works on Bloom Filters considered how to support insertions, deletions, membership queries, and multiplicity queries over (multi-)sets. In this paper, we introduce two novel algorithms for computing cardinalities of multi-sets represented by Bloom Filters, which extend the functionality of the Bloom Filter and thus make it usable in a variety of new applications. The Bloom structure presented in the previous work is used without any modification, and our algorithms have no influence to previous functionality. For Bloom Filters support cardinality computing in addition to insertions, deletions, membership queries, and multiplicity queries simultaneously, our work is a new step towards fully representing multi-sets by Bloom Filters. Performance analysis and experimental results show the difference of the two algorithms and show that our algorithms perform well in most cases.