eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-06-28
32:1
32:20
10.4230/LIPIcs.ICALP.2022.32
article
Improved Sublinear-Time Edit Distance for Preprocessed Strings
Bringmann, Karl
1
2
Cassis, Alejandro
1
2
Fischer, Nick
1
2
Nakos, Vasileios
3
Universität des Saarlandes, Saarland Informatics Campus, Saarbrücken, Germany
Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
RelationalAI, Berkeley, CA, USA
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 ⋅ n^o(1))-gap-gap edit distance in time (n/k + k) ⋅ n^o(1).
- After preprocessing both strings separately in time n^{1+o(1)}, we can solve (k, k ⋅ n^o(1))-gap edit distance in time kn^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 sublinear-time 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol229-icalp2022/LIPIcs.ICALP.2022.32/LIPIcs.ICALP.2022.32.pdf
Edit Distance
Property Testing
Preprocessing
Precision Sampling