# 臺灣博碩士論文加值系統

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 In this thesis we investigate the repeating group detection problems. We define a special kind of repeating groups, namely maximal repeating group. Based upon this definition, we define a special string, called complete repeating group string. Using dynamic programming method, we can find all repeating groups of a string, determine whether a string is a complete repeating group string and find all maximal repeating groups. By applying our algorithms to some DNA data, we detected one repeating group, with length 16036 of a DNA sequence. This shows that our algorithms may be helpful to biologists.
 Abstract iContents iiList of Figures iiiList of Table ivChapter 1 Introduction 11.1 Background and Motivation 11.2 Terminology 11.3 Thesis Organization 3Chapter 2 A Review of Related Research 42.1 The Longest Common Subsequence Problem 42.2 The Longest Palindrome Subsequence Problem 7Chapter 3 Problem 1 143.1 Algorithm 3.1 to Solve Problem 1 14Chapter 4 Problem 2 174.1. The Detection of Overlapping Repeating Groups and the Modification of the M Table 174.2 Algorithm 4.1 to Solve Problem 2 19Chapter 5 Problem 3 26Chapter 6 Experimental Results 32Chapter 7 Concluding Remarks 36Biblography 37Appendix I 39Appendix II 41Appendix III 46
 [AC75] Efficient String Matching, Matching, Aho A. V. and Corasick, M. J., Communications of ACM, Vol. 18, 1975, pp. 333-340.[B99] Tandem Repeats Finder: a Program to Analyze DNA Sequences, Benson, G., Oxford University Press, Vol. 27, 1999, pp. 573-580.[BD62] Applied Dynamic Programming, Bellman, R. and Dreyfus, S. E. , Princeton University Press, Princeton, New Jersey, 1962.[BJ2003] Detection and Visualization of Tandem Repeats in DNA Sequences, Buchner, M. and Janjarasjitt, S., IEEE Transactions on Signal Processing, Vol. 51, 2003, pp. 2280-2287.[BM77] A Fast String Searching Algorithm , Boyer, R. S and Moore, J. S. , Communication of the ACM , Vol. 20 , 1977 , pp. 762-772 .[CL88] The Multiple Sequence Alignment Problem in Biology, Carrillo, H. and Lipman, D., SIAM Journal on Applied Mathematics, Vol. 48, No. 5, 1988, pp. 1073-1082.[CWC92] A Survey of Multiple Sequence Comparison Methods, Chan, S. C., Wong, A. K. C. and Chiu, D. K. Y., Bulletin of Mathematical Biology, Vol. 54, No. 4, 1992, pp. 563-598.[FP74] String-Matching and other products, Fischer, M.M., and Paterson, M.S., SIAM-AMS Proceedings, Vol. 7., 1974, pp. 113-125.[G97] Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology, Gusfield, D., Cambridge University Press, 1997.[GG86] Improved String Matching with k Mismatches, Galil, Z. and Giancarlo, R., SIGACT News, Vol. 17, No. 4, 1986, pp. 52-54.[H94] On global sequence alignment, Huang, X., Bioinformatics, Vol. 10, No. 3, 1994, pp. 227-335.[H75] A Linear Space Algorithm for Computing Maximal Common Subsequences, Hirschberg, D. S. , Communications of the ACM, Vol. 18, No. 6, 1975, pp. 341-343.[KMP77] Fast Pattern Matching in Strings , Knuth, D. E., Morris, J. H. and Pratt, V. R. , SIAM Journal on Computing , Vol. 6 , 1977 , pp. 323-350.[LAK89] A Tool for Multiple Sequence Alignment, Lipman, D. J., Altschul, S. F. and Kececioglu, J. D., Proc. Nat. Acad. Sci., Vol. 86, 1989, pp. 4412-4415.[LV86] Efficient String Matching with k Mismatches, Landau, G. M. and Vishkin, U., Theoretical Computer Science, Vol. 43, 1986, pp. 239-149.[SG2002] Simple and flexible detection of contiguous repeats using a suffix tree, Stoye, J., Gusfield, D., Theoretical Computer Science, 2002.[SW81] Identification of Common Molecular Subsequences, Smith, T. F. and Waterman M. S., 1982, pp. 195-197.[U85] Algorithms for Approximate String Matching, E. Ukkonen, Information and Control, Vol. 64, 1985, pp. 100–118.[W2006]Longest Palindrome and Tandem Repeat Subsequences, Wen, W. H., 2006.[WLL2002] BALSA: Bayesian algorithm for local sequence alignment, Webb, B. M., Liu, J. S., and Lawrence, C. E., Nucleic Acids Research, Vol. 30, No. 5, pp. 1268-1277.[WYKG2004] Finding Approximate Tandem Repeats in Genomic Sequences, Wexler, Y., Yakhini, Z., Kashi, Y. and Geiger, D., Proceedings of the eighth annual international conference on Computational molecular biology, 2004, pp. 223-232.
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