Fast Dynamic Multiset Membership Testing Using Combinatorial Bloom Filters

In this paper we consider the problem of designing a data structure that can perform fast multiset membership testing in deterministic time. Our primary goal is to develop a hardware implementation of the data structure which uses only embedded memory blocks. Prior efforts to solve this problem involve hashing into multiple Bloom filters. Such approach needs a priori knowledge of the number of elements in each set in order to size the Bloom filter. We use a single Bloom filter based approach and use multiple sets of hash functions to code for the set (group) id. Since a single Bloom filter is used, it does not need a priori knowledge of the distribution of the elements across the different sets. We show how to improve the performance of the data structure by using constant weight error correcting codes for coding the group id. Using error correcting codes improves the performance of these data structures especially when there are large number of sets. We also outline an efficient hardware based approach to generate the the large number of hash functions that we need for this data structure. The resulting data structure, COMB, is amenable to a variety of time-critical network applications.