Near-linear time insertion-deletion codes and (1+ ε )-approximating edit distance via indexing
Bernhard Haeupler, Aviad Rubinstein, Amirbehshad Shahrasbi · 2019
We introduce fast-decodable indexing schemes for edit distance which can be used to speed up edit distance computations to near-linear time if one of the strings is indexed by an indexing string I. In particular, for every length n and every ε >0, one can in near linear time construct a string I ∈ Σ′n with |Σ′| = Oε(1), such that, indexing any string S ∈ Σn, symbol-by-symbol, with I results in a string S′ ∈ Σ″n where Σ″ = Σ × Σ′ for which edit distance computations are easy, i.e., one can compute a (1+ε)-approximation of the edit distance between S′ and any other string in O(n (logn)) time.