Pattern matching with address errors: Rearrangement distances

Historically, approximate pattern matching has mainly focused at coping with errors in the data, while the order of the text/pattern was assumed to be more or less correct. In this paper we consider a class of pattern matching problems where the content is assumed to be correct, while the locations may have shifted/changed. We formally define a broad class of problems of this type, capturing situations in which the pattern is obtained from the text by a sequence of rearrangements. We consider several natural rearrangement schemes, including the analogues of the ℓ₁ and ℓ₂ distances, as well as two distances based on interchanges. For these, we present efficient algorithms to solve the resulting string matching problems.