Improved SublinearTime Edit Distance for Preprocessed Strings
Abstract
We study the problem of approximating the edit distance of two strings in sublinear time, in a setting where one or both string(s) are preprocessed, as initiated by Goldenberg, Rubinstein, Saha (STOC '20). Specifically, in the $(k, K)$gap edit distance problem, the goal is to distinguish whether the edit distance of two strings is at most $k$ or at least $K$. We obtain the following results: * After preprocessing one string in time $n^{1+o(1)}$, we can solve $(k, k \cdot n^{o(1)})$gap edit distance in time $(n/k + k) \cdot n^{o(1)}$. * After preprocessing both strings separately in time $n^{1+o(1)}$, we can solve $(k, k \cdot n^{o(1)})$gap edit distance in time $k \cdot n^{o(1)}$. Both results improve upon some previously best known result, with respect to either the gap or the query time or the preprocessing time. Our algorithms build on the framework by Andoni, Krauthgamer and Onak (FOCS '10) and the recent sublineartime algorithm by Bringmann, Cassis, Fischer and Nakos (STOC '22). We replace many complicated parts in their algorithm by faster and simpler solutions which exploit the preprocessing.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 DOI:
 10.48550/arXiv.2204.14137
 arXiv:
 arXiv:2204.14137
 Bibcode:
 2022arXiv220414137B
 Keywords:

 Computer Science  Data Structures and Algorithms
 EPrint:
 Appears at ICALP '22