AnO(ND) difference algorithm and its variations

@article{Myers2005AnONDDA,
  title={AnO(ND) difference algorithm and its variations},
  author={Eugene W. Myers},
  journal={Algorithmica},
  year={2005},
  volume={1},
  pages={251-266}
}
  • E. Myers
  • Published 1 November 1986
  • Mathematics, Computer Science
  • Algorithmica
The problems of finding a longest common subsequence of two sequencesA andB and a shortest edit script for transformingA intoB have long been known to be dual problems. In this paper, they are shown to be equivalent to finding a shortest/longest path in an edit graph. Using this perspective, a simpleO(ND) time and space algorithm is developed whereN is the sum of the lengths ofA andB andD is the size of the minimum edit script forA andB. The algorithm performs well when differences are small… Expand
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References

SHOWING 1-10 OF 28 REFERENCES
A fast algorithm for computing longest common subsequences
TLDR
An algorithm for finding the longest common subsequence of two sequences of length n which has a running time of O((r + n) log n), where r is the total number of ordered pairs of positions at which the two sequences match. Expand
An Information-Theoretic Lower Bound for the Longest Common Subsequence Problem
  • D. Hirschberg
  • Computer Science, Mathematics
  • Inf. Process. Lett.
  • 1978
TLDR
An " oracle " or decision rule is defined by which a r ath, P,, is distinguished in each decision tree for the LCS problem by proving that n log II is a lower bound on the nunber of " less thanequal-greater than " comparisons requi't. Expand
A longest common subsequence algorithm suitable for similar text strings
TLDR
O(n(m-p) log n) algorithm is presented, and when p is close to m (in other words, two given strings are similar), the algorithm presented here runs much faster than previously known algorithms. Expand
Bounds on the Complexity of the Longest Common Subsequence Problem
TLDR
It is shown that unless a bound on the total number of distinct symbols is assumed, every solution to the problem can consume an amount of time that is proportional to the product of the lengths of the two strings. Expand
A Faster Algorithm Computing String Edit Distances
TLDR
An algorithm is described for computing the edit distance between two strings of length n and m, n ⪖ m, which requires O(n · max(1, mlog n) steps whenever the costs of edit operations are integral multiples of a single positive real number and the alphabet for the strings is finite. Expand
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. Expand
Fast Algorithms for Finding Nearest Common Ancestors
TLDR
An algorithm for a random access machine with uniform cost measure (and a bound of $\Omega (\log n)$ on the number of bits per word) that requires time per query and preprocessing time is presented, assuming that the collection of trees is static. Expand
Algorithms for the Longest Common Subsequence Problem
TLDR
A lgor i thm is appl icable in the genera l case and requi res O ( p n + n log n) t ime for any input strings o f lengths m and n even though the lower bound on T ime of O ( m n ) need not apply to all inputs. Expand
A note on two problems in connexion with graphs
  • E. Dijkstra
  • Mathematics, Computer Science
  • Numerische Mathematik
  • 1959
TLDR
A tree is a graph with one and only one path between every two nodes, where at least one path exists between any two nodes and the length of each branch is given. Expand
A Space-Economical Suffix Tree Construction Algorithm
A new algorithm is presented for constructing auxiliary digital search trees to aid in exact-match substring searching. This algorithm has the same asymptotic running time bound as previouslyExpand
...
1
2
3
...