Dictionary lookup with one genome evolution operation

Given anm-length query stringq, approximate dictionary lookup searches for strings in a string dictionaryDat a distance of 1 toqunder 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 inDthat can be generated fromqby one reversal or one transposition. When the length of the reversed substring is confined to a constant alpha>1, we propose anO(m)-time approach which usesO((|D|-alpha d)log|D|)bits space, where the dictionaryDhasdstrings with totally |D| symbols. If the lengths of the reversals are in a range [alpha,beta], the time for query isO((beta-alpha+1)mloglog|D|+occ), and the space isO(|D|log epsilon(|D|))words for any constant epsilon, in whichoccis the number of matched strings. For problems allowing one transposition, when the length of the transposition is fixed to alpha, the time for a dictionary lookup isO(alpha mloglog|D|+occ), while usingO(|D|log epsilon(|D|))words. In the case that the two swapped substrings are of the same length, the time for answering the query isO(m), while the space isO((|D|-alpha d)log|D|)bits.