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 certain… 
The string-to-string correction problem with block moves
TLDR
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.
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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
TLDR
The CELLAR algorithm is presented, and proof that ESSCP, with WI < WC = WD = @@@@, 0 < WS < @ @@@, suitably encoded, is NP-complete is proved.
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TLDR
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.
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TLDR
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
  • B. Oommen, R. Loke
  • Computer Science
    1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century
  • 1995
TLDR
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)
TLDR
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
TLDR
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.
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References

The String-to-String Correction Problem
TLDR
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.