LexicHash: sequence similarity estimation via lexicographic comparison of hashes

MOTIVATION: Pairwise sequence alignment is a heavy computational burden, particularly in the context of third-generation sequencing technologies. This issue is commonly addressed by approximately estimating sequence similarities using a hash-based method such as MinHash. In MinHash, all k-mers in a read are hashed and the minimum hash value, the min-hash, is stored. Pairwise similarities can then be estimated by counting the number of min-hash matches between a pair of reads, across many distinct hash functions. The choice of the parameter k controls an important tradeoff in the task of identifying alignments: larger k-values give greater confidence in the identification of alignments (high precision) but can lead to many missing alignments (low recall), particularly in the presence of significant noise. RESULTS: In this work, we introduce LexicHash, a new similarity estimation method that is effectively independent of the choice of k and attains the high precision of large-k and the high sensitivity of small-k MinHash. LexicHash is a variant of MinHash with a carefully designed hash function. When estimating the similarity between two reads, instead of simply checking whether min-hashes match (as in standard MinHash), one checks how “lexicographically similar” the LexicHash min-hashes are. In our experiments on 40 PacBio datasets, the area under the precision–recall curves obtained by LexicHash had an average improvement of 20.9% over MinHash. Additionally, the LexicHash framework lends itself naturally to an efficient search of the largest alignments, yielding an [Formula: see text] time algorithm, and circumventing the seemingly fundamental [Formula: see text] scaling associated with pairwise similarity search. AVAILABILITY AND IMPLEMENTATION: LexicHash is available on GitHub at https://github.com/gcgreenberg/LexicHash.