Article

Free access

On the complexity of the Extended String-to-String Correction Problem

Author:

Robert A. WagnerAuthors Info & Claims

STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

Pages 218 - 223

https://doi.org/10.1145/800116.803771

Published: 05 May 1975 Publication History

PDF eReader

Abstract

The Extended String-to-String Correction Problem [ESSCP] is defined as the problem of determining, for given strings A and B over alphabet V, a minimum-cost sequence S of edit operations such that S(A) = B. The sequence S may make use of the operations: Change, Insert, Delete and Swaps, each of constant cost W_C, W_I, W_D, and W_S respectively. Swap permits any pair of adjacent characters to be interchanged.

The principal results of this paper are:

(1) a brief presentation of an algorithm (the CELLAR algorithm) which solves ESSCP in time Ø(¦A¦* ¦B¦* ¦V¦^s*s), where s = min(4W_C, W_I+W_D)/W_S + 1;

(2) presentation of polynomial time algorithms for the cases (a) W_S = 0, (b) W_S > 0, W_C= W_I= W_D= @@@@;

(3) proof that ESSCP, with W_I < W_C = W_D = @@@@, 0 < W_S < @@@@, suitably encoded, is NP-complete. (The remaining case, W_S= @@@@, reduces ESSCP to the string-to-string correction problem of [1], where an Ø( ¦A¦* ¦B¦) algorithm is given.) Thus, “almost all” ESSCP's can be solved in deterministic polynomial time, but the general problem is NP-complete.

References

[1]

Wagner, R. A. & Fischer, M. J., "The string-to-string correction problem", Journal of the ACM, Vol. 21, no. l(January 1974), pp.168-173.

Digital Library

Google Scholar

[2]

Lowrance, R. & Wagner, R. A., "An extension of the string-to-string correction problem" to be published in the Journal of the ACM.

Digital Library

Google Scholar

[3]

Wagner, R. A. & Brown, T. P., "Swap-extended minimum edit distance correction for regular languages", Technical Report, Systems and Information Science Program, Vanderbilt University (January 1975).

Google Scholar

[4]

Karp, R. M., "Reducibility among combinatorial problems" in Complexity of Computer Computations, Miller, R. E. & Thatcher, J. W. (ed.), Plenum Press (1972), pp. 85-104.

Google Scholar

[5]

Wagner, R. A., "Generalized correction of context-free languages", Technical Report, Systems and Information Science Program, Vanderbilt Univeristy (1973).

Google Scholar

[6]

Gaver, G. P. & Thompson, G. L., Mathematical Models: Programming and Probability (1966).

Google Scholar

Cited By

View all

Cho MCho KNo K(2023)PhyloSophos: a high-throughput scientific name mapping algorithm augmented with explicit consideration of taxonomic science, and its application on natural product (NP) occurrence database processingBMC Bioinformatics10.1186/s12859-023-05588-324:1Online publication date: 14-Dec-2023
https://doi.org/10.1186/s12859-023-05588-3
Martyanov V(2022)Set-Theoretical Data Models in the Problem of Calculating Secondary Structures of RNASystem Analysis & Mathematical Modeling10.17150/2713-1734.2022.4(4).343-3574:4(343-357)Online publication date: 29-Dec-2022
https://doi.org/10.17150/2713-1734.2022.4(4).343-357
Kim YKang MJeong JKang DPark SSim J(2021)Reference Mapping Considering Swaps of Adjacent BasesApplied Sciences10.3390/app1111503811:11(5038)Online publication date: 29-May-2021
https://doi.org/10.3390/app11115038
Show More Cited By

Index Terms

On the complexity of the Extended String-to-String Correction Problem
1. Theory of computation
  1. Computational complexity and cryptography
    1. Problems, reductions and completeness
  2. Design and analysis of algorithms

Recommendations

The String-to-String Correction Problem

The string-to-string correction problem is to determine the distance between two strings as measured by the minimum cost sequence of “edit operations” needed to change the one string into the other. The edit operations investigated allow changing one ...
Constant-Time Randomized Parallel String Matching

Given a pattern string of length m for the string-matching problem, we design an algorithm that computes deterministic samples of a sufficiently long substring of the pattern in constant time. This problem used to be the bottleneck in the pattern ...
A three-string approach to the closest string problem

Given a set of n strings of length L and a radius d, the closest string problem (CSP for short) asks for a string t"s"o"l that is within a Hamming distance of d to each of the given strings. It is known that the problem is NP-hard and its optimization ...

Comments

Information & Contributors

Information

Published In

STOC '75: Proceedings of the seventh annual ACM symposium on Theory of computing

May 1975

265 pages

ISBN:9781450374194

DOI:10.1145/800116

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 May 1975

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Acceptance Rates

STOC '75 Paper Acceptance Rate 31 of 87 submissions, 36%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

62
Total Citations
View Citations
193
Total Downloads

Downloads (Last 12 months)62
Downloads (Last 6 weeks)10

Reflects downloads up to 01 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Cho MCho KNo K(2023)PhyloSophos: a high-throughput scientific name mapping algorithm augmented with explicit consideration of taxonomic science, and its application on natural product (NP) occurrence database processingBMC Bioinformatics10.1186/s12859-023-05588-324:1Online publication date: 14-Dec-2023
https://doi.org/10.1186/s12859-023-05588-3
Martyanov V(2022)Set-Theoretical Data Models in the Problem of Calculating Secondary Structures of RNASystem Analysis & Mathematical Modeling10.17150/2713-1734.2022.4(4).343-3574:4(343-357)Online publication date: 29-Dec-2022
https://doi.org/10.17150/2713-1734.2022.4(4).343-357
Kim YKang MJeong JKang DPark SSim J(2021)Reference Mapping Considering Swaps of Adjacent BasesApplied Sciences10.3390/app1111503811:11(5038)Online publication date: 29-May-2021
https://doi.org/10.3390/app11115038
Afshar RAmir AGoodrich MMatias P(2020)Adaptive Exact Learning in a Mixed-Up World: Dealing with Periodicity, Errors and Jumbled-Index Queries in String ReconstructionString Processing and Information Retrieval10.1007/978-3-030-59212-7_12(155-174)Online publication date: 17-Sep-2020
https://doi.org/10.1007/978-3-030-59212-7_12
Wang XWang L(2019)Computing Nonoverlapping Inversion Distance Between Two Strings in Linear Average TimeJournal of Computational Biology10.1089/cmb.2018.013626:3(193-201)Online publication date: Mar-2019
https://doi.org/10.1089/cmb.2018.0136
Fernau H(2019)Modern Aspects of Complexity Within Formal LanguagesLanguage and Automata Theory and Applications10.1007/978-3-030-13435-8_1(3-30)Online publication date: 14-Feb-2019
https://doi.org/10.1007/978-3-030-13435-8_1
Barbay JPérez-Lantero P(2018)Adaptive Computation of the Swap-Insert Correction DistanceACM Transactions on Algorithms10.1145/323205714:4(1-16)Online publication date: 9-Aug-2018
https://dl.acm.org/doi/10.1145/3232057
Barbay JOlivares A(2018)Indexed Dynamic Programming to Boost Edit Distance and LCSS ComputationString Processing and Information Retrieval10.1007/978-3-030-00479-8_6(61-73)Online publication date: 14-Sep-2018
https://doi.org/10.1007/978-3-030-00479-8_6
Hecht M(2017)A generalization of the most common subgraph distance and its application to graph editingPattern Recognition Letters10.1016/j.patrec.2016.09.00887:C(71-78)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1016/j.patrec.2016.09.008
Gao HNaeem MLutteroth CWeber GSong IGarcia-Alvarado COrdonez C(2015)S3JProceedings of the ACM Eighteenth International Workshop on Data Warehousing and OLAP10.1145/2811222.2811226(49-57)Online publication date: 22-Oct-2015
https://dl.acm.org/doi/10.1145/2811222.2811226
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

The String-to-String Correction Problem

Constant-Time Randomized Parallel String Matching

A three-string approach to the closest string problem

Comments

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Acceptance Rates

Other Metrics

Article Metrics

Other Metrics

Cited By

PDF

eReader

Login options

Full Access

Abstract

References

Cited By

Index Terms

Recommendations

The String-to-String Correction Problem

Constant-Time Randomized Parallel String Matching

A three-string approach to the closest string problem

Comments

Information

Published In

Sponsors

Publisher

Publication History

Permissions

Check for updates

Qualifiers

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations