MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

The Computational Hardness of Estimating Edit Distance

Author(s)
Andoni, Alexandr; Krauthgamer, Robert
Thumbnail
DownloadAndoni-2010-THE COMPUTATIONAL HA.pdf (431.1Kb)
PUBLISHER_POLICY

Publisher Policy

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.

Alternative title
THE COMPUTATIONAL HARDNESS OF ESTIMATING EDIT DISTANCE
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.
Metadata
Show full item record
Abstract
We prove the first nontrivial communication complexity lower bound for the problem of estimating the edit distance (aka Levenshtein distance) between two strings. To the best of our knowledge, this is the first computational setting in which the complexity of estimating the edit distance is provably larger than that of Hamming distance. Our lower bound exhibits a trade-off between approximation and communication, asserting, for example, that protocols with $O(1)$ bits of communication can obtain only approximation $\alpha\geq\Omega(\log d/\log\log d)$, where $d$ is the length of the input strings. This case of $O(1)$ communication is of particular importance since it captures constant-size sketches as well as embeddings into spaces like $l_1$ and squared-$l_2$, two prevailing algorithmic approaches for dealing with edit distance. Indeed, the known nontrivial communication upper bounds are all derived from embeddings into $l_1$. By excluding low-communication protocols for edit distance, we rule out a strictly richer class of algorithms than previous results. Furthermore, our lower bound holds not only for strings over a binary alphabet but also for strings that are permutations (aka the Ulam metric). For this case, our bound nearly matches an upper bound known via embedding the Ulam metric into $l_1$. Our proof uses a new technique that relies on Fourier analysis in a rather elementary way.
Date issued
2010-04
URI
http://hdl.handle.net/1721.1/58102
Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Journal
SIAM Journal of Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Andoni, Alexandr, and Robert Krauthgamer. “The Computational Hardness of Estimating Edit Distance.” SIAM Journal on Computing 39.6 (2010): 2398-2429. ©2010 Society for Industrial and Applied Mathematics.
Version: Final published version
ISSN
1095-7111
0097-5397

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.