Edit Distance Cannot Be Computed in Strongly Subquadratic Time (Unless SETH is False)
Name
15m1053128.pdf
Description
Published version
Size
328.37 KB
Format
Adobe PDF
Checksum (MD5)
4d6b25333fc5e37da69800d7b3db14f1
Author(s)
Backurs, Arturs
Indyk, Piotr
Date Issued
January 2018
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Backurs, Arturs and Indyk, Piotr. 2018. "Edit Distance Cannot Be Computed in Strongly Subquadratic Time (Unless SETH is False)." 47 (3).
Version
Final published version
Abstract
© 2018 Society for Industrial and Applied Mathematics. The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions, or substitutions of symbols needed to transform one string into another. The problem of computing the edit distance between two strings is a classical computational task, with a well-known algorithm based on dynamic programming. Unfortunately, all known algorithms for this problem run in nearly quadratic time. In this paper we provide evidence that the near-quadratic running time bounds known for the problem of computing edit distance might be tight. Specifically, we show that if the edit distance can be computed in time O(n2−δ) for some constant δ > 0, then the satisfiability of conjunctive normal form formulas with N variables and M clauses can be solved in time MO(1)2(1−)N for a constant > 0. The latter result would violate the strong exponential time hypothesis, which postulates that such algorithms do not exist.
Subjects
General Mathematics
General Computer Science
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/15m1053128
