Algorithms for subsequence combinatorics

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Algorithms for subsequence combinatorics
A subsequence is obtained from a string by deleting any number of characters; thus in contrast to a substring, a subsequence is not necessarily a contiguous part of the string. Counting subsequences under various constraints has become relevant to biological sequence analysis, to machine learning, to the analysis of categorical time series in the social sciences, and to the theory of word complexity. We present theorems that lead to efficient dynamic programming algorithms to count (1) distinct subsequences in a string, (2) distinct common subsequences of two strings, (3) matching joint embeddings in two strings, (4) distinct subsequences with a given minimum span, and (5) sequences generated by a string allowing characters to come in runs of a length that is bounded from above. Key words: subsequence, combinatorics, dynamic programming, algorithm, distinct, common, span, run, sociology, DNA sequencing, microarray
Cees H. Elzinga, Sven Rahmann, Hui Wang
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2008
Where TCS
Authors Cees H. Elzinga, Sven Rahmann, Hui Wang
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