Charalampopoulos, Panagiotis ;
Gawrychowski, Paweł ;
Mozes, Shay ;
Weimann, Oren
An Almost Optimal Edit Distance Oracle
Abstract
We consider the problem of preprocessing two strings S and T, of lengths m and n, respectively, in order to be able to efficiently answer the following queries: Given positions i,j in S and positions a,b in T, return the optimal alignment score of S[i..j] and T[a..b]. Let N = mn. We present an oracle with preprocessing time N^{1+o(1)} and space N^{1+o(1)} that answers queries in log^{2+o(1)}N time. In other words, we show that we can efficiently query for the alignment score of every pair of substrings after preprocessing the input for almost the same time it takes to compute just the alignment of S and T. Our oracle uses ideas from our distance oracle for planar graphs [STOC 2019] and exploits the special structure of the alignment graph. Conditioned on popular hardness conjectures, this result is optimal up to subpolynomial factors. Our results apply to both edit distance and longest common subsequence (LCS).
The best previously known oracle with construction time and size 𝒪(N) has slow Ω(√N) query time [Sakai, TCS 2019], and the one with size N^{1+o(1)} and query time log^{2+o(1)}N (using a planar graph distance oracle) has slow Ω(N^{3/2}) construction time [Long & Pettie, SODA 2021]. We improve both approaches by roughly a √ N factor.
BibTeX  Entry
@InProceedings{charalampopoulos_et_al:LIPIcs.ICALP.2021.48,
author = {Charalampopoulos, Panagiotis and Gawrychowski, Pawe{\l} and Mozes, Shay and Weimann, Oren},
title = {{An Almost Optimal Edit Distance Oracle}},
booktitle = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
pages = {48:148:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771955},
ISSN = {18688969},
year = {2021},
volume = {198},
editor = {Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
publisher = {Schloss Dagstuhl  LeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14117},
URN = {urn:nbn:de:0030drops141175},
doi = {10.4230/LIPIcs.ICALP.2021.48},
annote = {Keywords: longest common subsequence, edit distance, planar graphs, Voronoi diagrams}
}
02.07.2021
Keywords: 

longest common subsequence, edit distance, planar graphs, Voronoi diagrams 
Seminar: 

48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Issue date: 

2021 
Date of publication: 

02.07.2021 