Sublinear Algorithms for Gap Edit Distance

Elazar Goldenberg, Robert Krauthgamer, Barna Saha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The edit distance is a way of quantifying how similar two strings are to one another by counting the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. A simple dynamic programming computes the edit distance between two strings of length n in O(n2) time, and a more sophisticated algorithm runs in time O(n + t2) when the edit distance is t [Landau, Myers and Schmidt, SICOMP 1998]. In pursuit of obtaining faster running time, the last couple of decades have seen a flurry of research on approximating edit distance, including polylogarithmic approximation in near-linear time [Andoni, Krauthgamer and Onak, FOCS 2010], and a constant-factor approximation in subquadratic time [Chakrabarty, Das, Goldenberg, Koucḱy and Saks, FOCS 2018]. We study sublinear-Time algorithms for small edit distance, which was investigated extensively because of its numerous applications. Our main result is an algorithm for distinguishing whether the edit distance is at most t or at least t2 (the quadratic gap problem) in time Õ(n/t+t3). This time bound is sublinear roughly for all t in [ω(1), o(n1/3)], which was not known before. The best previous algorithms solve this problem in sublinear time only for t=ω(n1/3) [Andoni and Onak, STOC 2009]. Our algorithm is based on a new approach that adaptively switches between uniform sampling and reading contiguous blocks of the input strings. In contrast, all previous algorithms choose which coordinates to query non-Adaptively. Moreover, it can be extended to solve the t vs t2-ϵ gap problem in time Õ(n/t1-ϵ+t3).

Original languageEnglish
Title of host publicationProceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019
PublisherIEEE Computer Society
Pages1101-1120
Number of pages20
ISBN (Electronic)9781728149523
ISBN (Print)9781728149530
DOIs
StatePublished Online - 6 Jan 2020
Event60th IEEE Annual Symposium on Foundations of Computer Science (FOCS) - Baltimore, MD, United States
Duration: 9 Nov 201912 Nov 2019

Publication series

NameAnnual IEEE Symposium on Foundations of Computer Science
ISSN (Print)0272-5428

Conference

Conference60th IEEE Annual Symposium on Foundations of Computer Science (FOCS)
Period9/11/1912/11/19

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