Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false)

DOI10.1145/2746539.2746612zbMATH Open1321.68548arXiv1412.0348OpenAlexW2055693471MaRDI QIDQ2941488

Author name not available (Why is that?)

Publication date: 21 August 2015

Published in: (Search for Journal in Brave)

Abstract: 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 $O(n^{2-delta})$ for some constant $delta>0$, then the satisfiability of conjunctive normal form formulas with $N$ variables and $M$ clauses can be solved in time $M^{O(1)}{2}^{(1-epsilon)N}$ for a constant $epsilon>0$. The latter result would violate the Strong Exponential Time Hypothesis, which postulates that such algorithms do not exist.

Full work available at URL: https://arxiv.org/abs/1412.0348

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false)

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2941488)