Proceedings ArticleDOI
On the complexity of the Extended String-to-String Correction Problem
Robert A. Wagner
- pp 218-223
TLDR
The CELLAR algorithm is presented, and proof that ESSCP, with WI < WC = WD = @@@@, 0 < WS < @ @@@, suitably encoded, is NP-complete is proved.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 WC, WI, WD, and WS 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 O(¦A¦* ¦B¦* ¦V¦s*s), where s = min(4WC, WI+WD)/WS + 1; (2) presentation of polynomial time algorithms for the cases (a) WS = 0, (b) WS > 0, WC= WI= WD=read more
Citations
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The Tree-to-Tree Correction Problem
TL;DR: An algorithm is presented which solves the problem of determining the distance from T to T' as measured by the mlmmum cost sequence of edit operaUons needed to transform T into T'.
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Sequence analysis: new methods for old ideas
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Algorithms for the Longest Common Subsequence Problem
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Sequence Analysis and Optimal Matching Methods in Sociology Review and Prospect
Andrew Abbott,Angela Tsay +1 more
TL;DR: The authors reviewed all known studies applying optimal matching or alignment (OM) techniques to social science sequence data and concluded that OM techniques have produced interesting results in a wide variety of areas, the most promising being studies of careers and of sequentially organized cultural artifacts.
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The Complexity of Some Problems on Subsequences and Supersequences
TL;DR: It is shown that theyes/no version of the LCS problem is NP-complete for sequences over an alphabet of size 2, and that the yes/no SCS problem isNPcomplete for sequence over an Alphabet of size 5.
References
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Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Journal ArticleDOI
The String-to-String Correction Problem
TL;DR: 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.
Journal ArticleDOI
An Extension of the String-to-String Correction Problem
Robert A. Wagner,Roy Lowrance +1 more
TL;DR: The set of allowable edit operations is extended to include the operation of interchanging the positions of two adjacent characters under certain restrictions on edit-operation costs, and it is shown that the extended problem can still be solved in time proportional to the product of the lengths of the given strings.