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, t...

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Published inTheoretical computer science Vol. 409; no. 3; pp. 394 - 404
Main Authors Elzinga, Cees, Rahmann, Sven, Wang, Hui
Format Journal Article
LanguageEnglish
Published Oxford Elsevier B.V 28.12.2008
Elsevier
Subjects
Algorithm
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Dynamic programming
Exact sciences and technology
Learning and adaptive systems
Mathematics
Miscellaneous
Sciences and techniques of general use
Subsequence
Theoretical computing
Subsequence
Dynamic programming
Combinatorics
Algorithm
Word
Computer theory
Constraint
Social sciences
String matching
Time series
Embedding
Joint
Complexity
Coding theory
Character string
Coding
Dynamics
Counting
Online AccessGet full text
ISSN0304-3975
1879-2294
1879-2294
DOI10.1016/j.tcs.2008.08.035

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Abstract 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 coding theory, 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.
AbstractList 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 coding theory, 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.
Author Wang, Hui
Elzinga, Cees
Rahmann, Sven
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Cites_doi 10.1016/S0304-3975(98)00258-8
10.1006/jcta.2000.3081
10.36045/bbms/1102714173
10.1007/s00357-005-0007-6
10.37236/1761
10.1145/322033.322044
10.1016/0012-365X(76)90140-0
10.1007/s10680-007-9133-7
10.1515/dma.1992.2.3.241
10.1109/TIT.2002.806155
10.1016/S0304-3975(98)00248-5
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Issue 3
Keywords Subsequence
Dynamic programming
Combinatorics
Algorithm
Word
Computer theory
Constraint
Social sciences
String matching
Time series
Embedding
Joint
Complexity
Coding theory
Character string
Coding
Dynamics
Counting
Language English
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References Swart, Ferreira (b28) 2003; 49
Salomaa (b27) 2003
Andrews (b1) 1998
Levenshtein (b21) 1992; 2
Crochemore, Rytter (b6) 1994
Chase (b5) 1976; 16
Levé, Séébold (b19) 2001; 8
Lothaire (b24) 2002; vol. 90
2003
Levenshtein (b20) 1966; 10
Ferenczi, Kása (b11) 1999; 218
Hirschberg, Regnier (b16) 2000; 1
H. Wang, All common subsequences, in: M.M. Veloso (Ed.), IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, 2007
Bergroth, Hakonen, Väisänen (b4) 2003
de Luca (b7) 1999; 218
Hirschberg (b15) 1977; 24
cs.DS
Iványi (b17) 1987; 8
Bergroth, Hakonen, Raita (b3) 2000
Flaxman, Harrow, Sorkin (b12) 2004; 11
C.H. Elzinga, Turbulence in categorical time series, Sociological Methods & Research (submitted for publication)
Elzinga, Liefbroer (b10) 2007; 23
Anisiu, Blázsik, Kása (b2) 2002; 13
Gusfield (b14) 1997
Rahmann (b25) 2006; vol. 4009
Elzinga (b8) 2005; 22
Kása (b18) 1998; 9
Levenshtein (b22) 2001; 93
Lothaire (b23) 1983; vol. 17
R.I. Greenberg, Computing the number of longest common subsequences, Computational Science Research Repository.
Sakarovitch, Simon (b26) 1983
Kása (10.1016/j.tcs.2008.08.035_b18) 1998; 9
Elzinga (10.1016/j.tcs.2008.08.035_b8) 2005; 22
Chase (10.1016/j.tcs.2008.08.035_b5) 1976; 16
Andrews (10.1016/j.tcs.2008.08.035_b1) 1998
Elzinga (10.1016/j.tcs.2008.08.035_b10) 2007; 23
10.1016/j.tcs.2008.08.035_b29
Salomaa (10.1016/j.tcs.2008.08.035_b27) 2003
Hirschberg (10.1016/j.tcs.2008.08.035_b16) 2000; 1
Levenshtein (10.1016/j.tcs.2008.08.035_b20) 1966; 10
de Luca (10.1016/j.tcs.2008.08.035_b7) 1999; 218
Bergroth (10.1016/j.tcs.2008.08.035_b4) 2003
Crochemore (10.1016/j.tcs.2008.08.035_b6) 1994
Sakarovitch (10.1016/j.tcs.2008.08.035_b26) 1983
Gusfield (10.1016/j.tcs.2008.08.035_b14) 1997
Levé (10.1016/j.tcs.2008.08.035_b19) 2001; 8
Levenshtein (10.1016/j.tcs.2008.08.035_b21) 1992; 2
10.1016/j.tcs.2008.08.035_b9
Ferenczi (10.1016/j.tcs.2008.08.035_b11) 1999; 218
Anisiu (10.1016/j.tcs.2008.08.035_b2) 2002; 13
10.1016/j.tcs.2008.08.035_b13
Lothaire (10.1016/j.tcs.2008.08.035_b23) 1983; vol. 17
Bergroth (10.1016/j.tcs.2008.08.035_b3) 2000
Lothaire (10.1016/j.tcs.2008.08.035_b24) 2002; vol. 90
Flaxman (10.1016/j.tcs.2008.08.035_b12) 2004; 11
Hirschberg (10.1016/j.tcs.2008.08.035_b15) 1977; 24
Swart (10.1016/j.tcs.2008.08.035_b28) 2003; 49
Rahmann (10.1016/j.tcs.2008.08.035_b25) 2006; vol. 4009
Levenshtein (10.1016/j.tcs.2008.08.035_b22) 2001; 93
Iványi (10.1016/j.tcs.2008.08.035_b17) 1987; 8
References_xml – year: 1998
  ident: b1
  article-title: The Theory of Partitions
– reference: [cs.DS] (
– volume: 13
  start-page: 39
  year: 2002
  end-page: 48
  ident: b2
  article-title: Maximal Complexity of Finite Words
  publication-title: Pure Mathematics and Applications
– start-page: 287
  year: 2003
  end-page: 303
  ident: b4
  article-title: New refinement techniques for longest common subsequence algorithms
  publication-title: String processing and Information Retrieval, 10th International Symposium
– reference: R.I. Greenberg, Computing the number of longest common subsequences, Computational Science Research Repository.
– volume: 49
  start-page: 269
  year: 2003
  end-page: 273
  ident: b28
  article-title: A note on double insertion/deletion correcting codes
  publication-title: IEEE Transaction on Information Theory
– volume: 8
  start-page: 69
  year: 1987
  end-page: 90
  ident: b17
  article-title: On the
  publication-title: Sectio Computatorica
– start-page: 165
  year: 2003
  end-page: 179
  ident: b27
  article-title: Counting (scatterred) subwords
  publication-title: Bulletin of the European Association for Theoretical Computer Science
– year: 1994
  ident: b6
  article-title: Text Algorithms
– volume: 218
  start-page: 13
  year: 1999
  end-page: 39
  ident: b7
  article-title: On the combinatorics of finite words
  publication-title: Theoretical Computer Science
– start-page: 39
  year: 2000
  end-page: 48
  ident: b3
  article-title: A survey of longest common subsequence algorithms
  publication-title: Proceedings of the Seventh International Symposium on String Processing and Information Retrieval
– year: 1997
  ident: b14
  article-title: Algorithms on Strings, Trees and Sequences, Computer Science and Computational Biology
– reference: H. Wang, All common subsequences, in: M.M. Veloso (Ed.), IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, 2007
– volume: 22
  start-page: 87
  year: 2005
  end-page: 118
  ident: b8
  article-title: Combinatorial representation of token sequences
  publication-title: Journal of Classification
– volume: 11
  start-page: R8
  year: 2004
  ident: b12
  article-title: Strings with maximally many distict subsequences and substrings
  publication-title: The Electronic Journal of Combinatorics
– volume: 9
  start-page: 119
  year: 1998
  end-page: 128
  ident: b18
  article-title: On the d-complexity of strings
  publication-title: Pure Mathematics and Applications
– reference: C.H. Elzinga, Turbulence in categorical time series, Sociological Methods & Research (submitted for publication)
– volume: 93
  start-page: 310
  year: 2001
  end-page: 332
  ident: b22
  article-title: Efficient reconstruction of sequences from their subsequences or supersequences
  publication-title: Journal of Combinatorial Theory, Series A
– volume: 218
  start-page: 177
  year: 1999
  end-page: 195
  ident: b11
  article-title: Complexity for finite factors of infinite sequences
  publication-title: Theoretical Computer Science
– volume: 2
  start-page: 241
  year: 1992
  end-page: 258
  ident: b21
  article-title: On perfect codes in insertion and deletion metric
  publication-title: Discrete Mathematics and Applications
– year: 1983
  ident: b26
  article-title: Subwords
  publication-title: Combinatorics on Words
– volume: 10
  start-page: 707
  year: 1966
  end-page: 710
  ident: b20
  article-title: Binary codes capable of correcting deletions, insertions and reversals
  publication-title: Soviet Physics Doklady
– volume: 16
  start-page: 123
  year: 1976
  end-page: 140
  ident: b5
  article-title: Subsequence numbers and logarithmic concavity
  publication-title: Discrete Mathematics
– volume: vol. 17
  year: 1983
  ident: b23
  publication-title: Combinatorics on Words
– volume: 23
  start-page: 225
  year: 2007
  end-page: 250
  ident: b10
  article-title: De-standardization and differentiation of family life trajectories of young adults: A cross-national comparison using sequence analysis
  publication-title: European Journal of Population
– volume: 24
  start-page: 664
  year: 1977
  end-page: 675
  ident: b15
  article-title: Algorithms for the longest common subsequence problem
  publication-title: Journal of the ACM
– volume: vol. 90
  year: 2002
  ident: b24
  publication-title: Algebraic Combinatorics on Words
– volume: 8
  start-page: 277
  year: 2001
  end-page: 291
  ident: b19
  article-title: Proof of a conjecture on word complexity
  publication-title: Bulletin of the Belgian Mathematical Society Simon Stevin
– reference: ), 2003
– volume: vol. 4009
  start-page: 153
  year: 2006
  end-page: 164
  ident: b25
  article-title: Subsequence combinatorics and applications to microarray production, DNA sequencing and chaining algorithms
  publication-title: Combinatorial Pattern Matching (CPM)
– volume: 1
  start-page: 123
  year: 2000
  end-page: 132
  ident: b16
  article-title: Tight bounds on the number of string subsequences
  publication-title: Journal of Discrete Algorithms
– start-page: 287
  year: 2003
  ident: 10.1016/j.tcs.2008.08.035_b4
  article-title: New refinement techniques for longest common subsequence algorithms
– volume: 8
  start-page: 69
  year: 1987
  ident: 10.1016/j.tcs.2008.08.035_b17
  article-title: On the d-complexity of words, Annales ”Universitatis Scientiarum Budapestinensis de Rolando Eötvös nominatae
  publication-title: Sectio Computatorica
– ident: 10.1016/j.tcs.2008.08.035_b13
– ident: 10.1016/j.tcs.2008.08.035_b9
– year: 1997
  ident: 10.1016/j.tcs.2008.08.035_b14
– start-page: 165
  issue: 81
  year: 2003
  ident: 10.1016/j.tcs.2008.08.035_b27
  article-title: Counting (scatterred) subwords
  publication-title: Bulletin of the European Association for Theoretical Computer Science
– volume: 9
  start-page: 119
  issue: 1–2
  year: 1998
  ident: 10.1016/j.tcs.2008.08.035_b18
  article-title: On the d-complexity of strings
  publication-title: Pure Mathematics and Applications
– year: 1994
  ident: 10.1016/j.tcs.2008.08.035_b6
– volume: 10
  start-page: 707
  year: 1966
  ident: 10.1016/j.tcs.2008.08.035_b20
  article-title: Binary codes capable of correcting deletions, insertions and reversals
  publication-title: Soviet Physics Doklady
– ident: 10.1016/j.tcs.2008.08.035_b29
– volume: 218
  start-page: 177
  year: 1999
  ident: 10.1016/j.tcs.2008.08.035_b11
  article-title: Complexity for finite factors of infinite sequences
  publication-title: Theoretical Computer Science
  doi: 10.1016/S0304-3975(98)00258-8
– volume: 93
  start-page: 310
  issue: 2
  year: 2001
  ident: 10.1016/j.tcs.2008.08.035_b22
  article-title: Efficient reconstruction of sequences from their subsequences or supersequences
  publication-title: Journal of Combinatorial Theory, Series A
  doi: 10.1006/jcta.2000.3081
– volume: 8
  start-page: 277
  issue: 2
  year: 2001
  ident: 10.1016/j.tcs.2008.08.035_b19
  article-title: Proof of a conjecture on word complexity
  publication-title: Bulletin of the Belgian Mathematical Society Simon Stevin
  doi: 10.36045/bbms/1102714173
– volume: 22
  start-page: 87
  issue: 1
  year: 2005
  ident: 10.1016/j.tcs.2008.08.035_b8
  article-title: Combinatorial representation of token sequences
  publication-title: Journal of Classification
  doi: 10.1007/s00357-005-0007-6
– year: 1983
  ident: 10.1016/j.tcs.2008.08.035_b26
  article-title: Subwords
– volume: vol. 17
  year: 1983
  ident: 10.1016/j.tcs.2008.08.035_b23
– volume: 11
  start-page: R8
  year: 2004
  ident: 10.1016/j.tcs.2008.08.035_b12
  article-title: Strings with maximally many distict subsequences and substrings
  publication-title: The Electronic Journal of Combinatorics
  doi: 10.37236/1761
– volume: 1
  start-page: 123
  issue: 1
  year: 2000
  ident: 10.1016/j.tcs.2008.08.035_b16
  article-title: Tight bounds on the number of string subsequences
  publication-title: Journal of Discrete Algorithms
– year: 1998
  ident: 10.1016/j.tcs.2008.08.035_b1
– volume: 13
  start-page: 39
  issue: 1–2
  year: 2002
  ident: 10.1016/j.tcs.2008.08.035_b2
  article-title: Maximal Complexity of Finite Words
  publication-title: Pure Mathematics and Applications
– volume: vol. 4009
  start-page: 153
  year: 2006
  ident: 10.1016/j.tcs.2008.08.035_b25
  article-title: Subsequence combinatorics and applications to microarray production, DNA sequencing and chaining algorithms
– volume: 24
  start-page: 664
  issue: 4
  year: 1977
  ident: 10.1016/j.tcs.2008.08.035_b15
  article-title: Algorithms for the longest common subsequence problem
  publication-title: Journal of the ACM
  doi: 10.1145/322033.322044
– volume: 16
  start-page: 123
  year: 1976
  ident: 10.1016/j.tcs.2008.08.035_b5
  article-title: Subsequence numbers and logarithmic concavity
  publication-title: Discrete Mathematics
  doi: 10.1016/0012-365X(76)90140-0
– volume: 23
  start-page: 225
  issue: 3–4
  year: 2007
  ident: 10.1016/j.tcs.2008.08.035_b10
  article-title: De-standardization and differentiation of family life trajectories of young adults: A cross-national comparison using sequence analysis
  publication-title: European Journal of Population
  doi: 10.1007/s10680-007-9133-7
– volume: vol. 90
  year: 2002
  ident: 10.1016/j.tcs.2008.08.035_b24
– volume: 2
  start-page: 241
  issue: 3
  year: 1992
  ident: 10.1016/j.tcs.2008.08.035_b21
  article-title: On perfect codes in insertion and deletion metric
  publication-title: Discrete Mathematics and Applications
  doi: 10.1515/dma.1992.2.3.241
– volume: 49
  start-page: 269
  issue: 1
  year: 2003
  ident: 10.1016/j.tcs.2008.08.035_b28
  article-title: A note on double insertion/deletion correcting codes
  publication-title: IEEE Transaction on Information Theory
  doi: 10.1109/TIT.2002.806155
– start-page: 39
  year: 2000
  ident: 10.1016/j.tcs.2008.08.035_b3
  article-title: A survey of longest common subsequence algorithms
– volume: 218
  start-page: 13
  year: 1999
  ident: 10.1016/j.tcs.2008.08.035_b7
  article-title: On the combinatorics of finite words
  publication-title: Theoretical Computer Science
  doi: 10.1016/S0304-3975(98)00248-5
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Snippet 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...
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Enrichment Source
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StartPage 394
SubjectTerms Algorithm
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Dynamic programming
Exact sciences and technology
Learning and adaptive systems
Mathematics
Miscellaneous
Sciences and techniques of general use
Subsequence
Theoretical computing
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Title Algorithms for subsequence combinatorics
URI https://dx.doi.org/10.1016/j.tcs.2008.08.035
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