Abstract
The Multidimensional Longest Increasing Subsequence (MLIS) and Multidimensional Common Longest Increasing Subsequence (MCLIS) have their importance in many data mining applications. This work finds all increasing subsequences in n sliding window, longest increasing sequences in one and more sequences, decreasing subsequences and common increasing sequences of varied window sizes with one or more dimensions. The proposed work can be applied to finding diverging patterns, constraint MLIS, sequence alignment, find motifs in genetic databases, pattern recognition, mine emerging patterns, and contrast patterns in both, scientific and commercial databases. The algorithms are implemented and tested for accuracy in both real and simulated databases. Finally, the validity of the algorithms are checked and their time complexity are analyzed.
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References
Murugan, A., Lavanya, B.: A DNA algorithmic approach to solve GCS problem. Journal of Computational Intelligence in Bioinformatics 3(2), 239–247 (2010)
Murugan, A., Lavanya, B., Shyamala, K.: A novel programming approach for DNA computing. International Journal of Computational Intelligence Research 7(2), 199–209 (2011)
Delcher, A.L., Kasif, S., Feischmann, R.D., Peterson, J., White, O., Salzberg, S.L.: Alignment of whole genomes. Nucleic Acids Research 27, 2369–2376 (1999)
Lavanya, B., Murugan, A.: A DNA based approach to find closed repetitive gapped subsequence from a sequence database. International Journal of Computer Applications 29(5), 45–49 (2011)
Lavanya, B., Murugan, A.: Discovery of longest increasing subsequences and its variants using DNA operations. International Journal of Engineering and Technology 5(2), 1169–1177 (2013)
Lavanya, B., Murugan, A.: Multidimensional longest common subsequence discovery from large databases using DNA operations. International Journal of Engineering and Technology 5(2), 1153–1160 (2013)
Schensted, C.: Longest increasing and decreasing subsequences. Can. J. Math 13, 179–191 (1961)
Crochemore, M., Porat, E.: Fast computation of longest increasing subsequences and application. Information and Computation 208, 1054–1059 (2010)
Knuth, D.E.: Permutations,matricesand generalized young tableaux. Pacific. J. Math 34, 709–727 (1970)
Esmaieli, M., Tarafdar, M.: Sequential pattern mining from multidimensional sequence data in parallel. International Journal of Computer Theory and Engineering 2(5), 730–733 (2010)
Hirosawa, et al.: Comprehensive study on iterative algorithms of multiple sequence alignment. Computational Applications in Biosciences 11, 13–18 (1995)
De B. Robinson, G.: On representation of symmetric group. Am. J. Math 60, 745–760 (1938)
Fredman, M.L.: On computing the length of longest increasing subsequences. Discrete Mathematics 11(1), 29–35 (1975)
Wang, L., Jiang, T.: On the complexity of multiple sequence alignment. Journal of Computational Biology 1, 337–348 (1994)
Tompa, M.: An exact method for finding short motifs in sequences with application to ribisome binding site problem. In: Proc. Seventh Int’l. Conf. Intelligent Systems for Molecular Biology, pp. 262–271 (1999)
Bespamyatnikh, S., Segal, M.: Enumerating longest increasing subsequences and patience sorting. Information Processing Letters 76(1-2), 7–11 (2000)
Hunt, J.W., Szymanski, T.G.: A fast algorithm for computing longest common subsequences. Communications of ACM 20(5), 350–353 (1977)
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Lavanya, B., Murugan, A. (2013). Multidimensional Longest Increasing Subsequences and Its Variants Discovery Using DNA Operations. In: Prasath, R., Kathirvalavakumar, T. (eds) Mining Intelligence and Knowledge Exploration. Lecture Notes in Computer Science(), vol 8284. Springer, Cham. https://doi.org/10.1007/978-3-319-03844-5_45
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DOI: https://doi.org/10.1007/978-3-319-03844-5_45
Publisher Name: Springer, Cham
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