Dictionary lookup with one genome evolution operation

Abstract

SummaryGiven an m‐length query string q, approximate dictionary lookup searches for strings in a string dictionary D at a distance of 1 to q under some distances. In biological retrieval systems, the distances in such queries are defined by evolution operations on genomes. We consider the approximate dictionary lookup with one genome evolution operation including reversal and transposition, which searches for strings in D that can be generated from q by one reversal or one transposition. When the length of the reversed substring is confined to a constant α>1, we propose an O(m)‐time approach which uses bits space, where the dictionary D has d strings with totally |D| symbols. If the lengths of the reversals are in a range [α,β], the time for query is , and the space is words for any constant ε, in which occ is the number of matched strings. For problems allowing one transposition, when the length of the transposition is fixed to α, the time for a dictionary lookup is , while using words. In the case that the two swapped substrings are of the same length, the time for answering the query is O(m), while the space is bits.