# An Extension of the String-to-String Correction Problem

@article{Lowrance1975AnEO, title={An Extension of the String-to-String Correction Problem}, author={Roy Lowrance and Robert A. Wagner}, journal={J. ACM}, year={1975}, volume={22}, pages={177-183} }

The string-to-string correction problem asks for a sequence S of "edit operations" of minimal cost such that ~(A) = B, for given strings A and B. The edit operations previously investi- gated allow changing one symbol of a string into another single symbol, deleting one symbol from a string, or inserting a single symbol into a string. This paper extends the set of allowable edit opera- tions to include the operation of interchanging the positions of two adjacent characters Under certainâ€¦Â

## 344 Citations

The string-to-string correction problem with block moves

- Computer ScienceTOCS
- 1984

An algorithm that produces the shortest edit sequence transforming one string into another is presented and is optimal in the sense that it generates a minimal covering set of common substrings of one string with respect to another.

The Binary String-to-String Correction Problem

- Computer Science
- 2013

This thesis presents the first careful examination of the binary-alphabet case of String-to-String Correction, and presents several special cases of BSSC for which an optimal solution can be found in polynomial time; in particular, the case where T and M have an equal number of occurrences of a given symbol has a polyn coefficients time solution.

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

- Computer ScienceSTOC
- 1975

The CELLAR algorithm is presented, and proof that ESSCP, with WI < WC = WD = @@@@, 0 < WS < @ @@@, suitably encoded, is NP-complete is proved.

Charge and reduce: A fixed-parameter algorithm for String-to-String Correction

- Computer ScienceDiscret. Optim.
- 2010

The string merging problem

- Mathematics, Computer ScienceBIT
- 1981

A special case where deletion is the only allowed edition operation is shown to have the longest common subsequence of the strings as its solution.

A string correction method based on the context-dependent similarity

- Computer Science
- 1988

The invariance of the similarity to parallel transformations, a separation theorem and topological equivalence are described and the string-tostring correction problem based on the context-dependent edit operations is described.

Pattern recognition of strings containing traditional and generalized transposition errors

- Computer Science1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century
- 1995

This paper presents the first reported solution to the analytic problem of editing one string X to another, Y using these four edit operations using a syntactic pattern recognition scheme which corrects noisy text containing all these types of errors.

Efficient Algorithms for Approximate String Matching with Swaps (Extended Abstract)

- Computer ScienceCPM
- 1997

This paper includes the swap operation that interchanges two adjacent characters into the set of allowable edit operations, and presents an O(t min(m,n)-time algorithm for the extended edit distance problem, where t is the edit distance between the given strings.

Efficient Algorithms for Approximate String Matching with Swaps

- Computer ScienceJ. Complex.
- 1999

This paper includes the swapoperation that interchanges two adjacent characters into the set of allowable edit operations, and presents anO(tmin(m,n))-time algorithm for the extended edit distance problem, where tmin represents the edit distance between the given strings, and n represents the extendedk-differences problem.

## References

The String-to-String Correction Problem

- Mathematics, EducationJACM
- 1974

An algorithm is presented which solves the string-to-string correction problem in time proportional to the product of the lengths of the two strings.