2,353 research outputs found
Bounds on the Number of Longest Common Subsequences
This paper performs the analysis necessary to bound the running time of
known, efficient algorithms for generating all longest common subsequences.
That is, we bound the running time as a function of input size for algorithms
with time essentially proportional to the output size. This paper considers
both the case of computing all distinct LCSs and the case of computing all LCS
embeddings. Also included is an analysis of how much better the efficient
algorithms are than the standard method of generating LCS embeddings. A full
analysis is carried out with running times measured as a function of the total
number of input characters, and much of the analysis is also provided for cases
in which the two input sequences are of the same specified length or of two
independently specified lengths.Comment: 13 pages. Corrected typos, corrected operation of hyperlinks,
improved presentatio
Computing the Number of Longest Common Subsequences
This note provides very simple, efficient algorithms for computing the number
of distinct longest common subsequences of two input strings and for computing
the number of LCS embeddings.Comment: 3 pages, LaTe
Faster Approximate String Matching for Short Patterns
We study the classical approximate string matching problem, that is, given
strings and and an error threshold , find all ending positions of
substrings of whose edit distance to is at most . Let and
have lengths and , respectively. On a standard unit-cost word RAM with
word size we present an algorithm using time When is
short, namely, or this
improves the previously best known time bounds for the problem. The result is
achieved using a novel implementation of the Landau-Vishkin algorithm based on
tabulation and word-level parallelism.Comment: To appear in Theory of Computing System
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