Mercury BLAST dictionaries: analysis and performance measurement

This report describes a hashing scheme for a dictionary of short bit strings. The scheme, which we call near-perfect hashing, was designed as part of the construction of Mercury BLAST, an FPGA-based accelerator for the BLAST family of biosequence comparison algorithms. Near-perfect hashing is a heuristic variant of the well-known displacement hashing approach to building perfect hash functions. It uses a family of hash functions composed from linear transformations on bit vectors and lookups in small precomputed tables, both of which are especially appropriate for implementation in ardware logic. We show empirically that for inputs derived from genomic DNA sequences, our scheme obtains a good tradeoff between the size of the hash table and the time required to ompute it from a set of input strings, while generating few or no collisions between keys in the table. One of the building blocks of our scheme is the H_3 family of hash functions, which are linear transformations on bit vectors. We show that the uniformity of hashing performed with randomly chosen linear transformations depends critically on their rank, and that randomly chosen transformations have a high probability of having the Type of Report: Other Department of Computer Science & Engineering Washington University in St. Louis Campus Box 1045 St. Louis, MO 63130 ph: (314) 935-6160 Mercury BLAST Dictionaries: Analysis and Performance Measurement Jeremy Buhler [email protected]