Finite automata based algorithms on subsequences and supersequences of degenerate strings

In this paper, we present linear-time algorithms for the construction two novel types of finite automata and show how they can be used to efficiently solve the Longest Common Subsequence (LCS), Shortest Common Supersequence (SCS) and Constrained Longest Common Subsequence (CLCS) problems for degenerate strings.

[1]  Wojciech Rytter,et al.  Algorithms for Two Versions of LCS Problem for Indeterminate Strings , 2007 .

[2]  Alfredo De Santis,et al.  A simple algorithm for the constrained sequence problems , 2004, Information Processing Letters.

[3]  L. Bergroth,et al.  A survey of longest common subsequence algorithms , 2000, Proceedings Seventh International Symposium on String Processing and Information Retrieval. SPIRE 2000.

[4]  Borivoj Melichar,et al.  Directed Acyclic Subsequence Graph , 1998, Stringology.

[5]  Ömer Egecioglu,et al.  Algorithms For The Constrained Longest Common Subsequence Problems , 2005, Int. J. Found. Comput. Sci..

[6]  D Sankoff,et al.  A test for nucleotide sequence homology. , 1973, Journal of molecular biology.

[7]  Stephen Y. Itoga The string merging problem , 1981, BIT.

[8]  Dan Gusfield,et al.  Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology , 1997 .

[9]  R. J. Nelson,et al.  Introduction to Automata , 1968 .

[10]  David Maier,et al.  The Complexity of Some Problems on Subsequences and Supersequences , 1978, JACM.

[11]  Michael Rodeh,et al.  Linear Algorithm for Data Compression via String Matching , 1981, JACM.

[12]  Tao Jiang,et al.  On the Approximation of Shortest Common Supersequences and Longest Common Subsequences , 1995, SIAM J. Comput..

[13]  Dan Gusfield,et al.  Algorithms on strings , 1997 .

[14]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[15]  Helmut Rzehak,et al.  Languages and translation techniques for extensive use of parallel operations , 2005, Computing.

[16]  King-Sun Fu,et al.  A Sentence-to-Sentence Clustering Procedure for Pattern Analysis , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[18]  Michael J. Fischer,et al.  The String-to-String Correction Problem , 1974, JACM.

[19]  Ricardo A. Baeza-Yates,et al.  Searching Subsequences , 1991, Theor. Comput. Sci..

[20]  Ronald L. Rivest,et al.  Introduction to Algorithms, third edition , 2009 .

[21]  Robert A. Wagner,et al.  An Extension of the String-to-String Correction Problem , 1975, JACM.

[22]  Maxime Crochemore,et al.  Calcul de La Distance Par Les Sous-Mots , 1986, RAIRO Theor. Informatics Appl..

[23]  Costas S. Iliopoulos,et al.  New efficient algorithms for the LCS and constrained LCS problems , 2008, Inf. Process. Lett..

[24]  Yin-Te Tsai,et al.  The constrained longest common subsequence problem , 2003, Inf. Process. Lett..