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Title: Near-linear time insertion-deletion codes and (1+ ε)-approximating edit distance via indexing
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 (log n)) time. Our indexing schemes can be used to improve the decoding complexity of state-of-the-art error correcting codes for insertions and deletions. In particular, they lead to near-linear time decoding algorithms for the insertion-deletion codes of [Haeupler, Shahrasbi; STOC ‘17] and faster decoding algorithms for list-decodable insertion-deletion codes of [Haeupler, Shahrasbi, Sudan; ICALP ‘18]. Interestingly, the latter codes are a crucial ingredient in the construction of fast-decodable indexing schemes.  more » « less
Award ID(s):
1910588 1814603 1750808 1618280
NSF-PAR ID:
10121505
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
ACM Symposium on Theory of Computing
Page Range / eLocation ID:
697 to 708
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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