Learning locality-sensitive bucketing functions

Many tasks in sequence analysis ask to identify biologically related sequences in a large set. The edit distance, being a sensible model for both evolution and sequencing error, is widely used in these tasks as a measure. The resulting computational problem-to recognize all pairs of sequences within a small edit distance-turns out to be exceedingly difficult, since the edit distance is known to be notoriously expensive to compute and that all-versus-all comparison is simply not acceptable with millions or billions of sequences. Among many attempts, we recently proposed the locality-sensitive bucketing (LSB) functions to meet this challenge. Formally, a (d1,d2)-LSB function sends sequences into multiple buckets with the guarantee that pairs of sequences of edit distance at most d1 can be found within a same bucket while those of edit distance at least d2 do not share any. LSB functions generalize the locality-sensitive hashing (LSH) functions and admit favorable properties, with a notable highlight being that optimal LSB functions for certain (d1,d2) exist. LSB functions hold the potential of solving above problems optimally, but the existence of LSB functions for more general (d1,d2) remains unclear, let alone constructing them for practical use.