A Study on the Longest Common Subsequence Problem
碩士 === 靜宜大學 === 資訊管理學系研究所 === 90 === The longest common subsequence (LCS) problem is a famous NP-Hard problem, which is to find the longest common subsequence on a set S of n strings of length m over an alphabet setΣ. This problem has many important applications in different areas. One important app...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2002
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| Online Access: | http://ndltd.ncl.edu.tw/handle/32031865936838986775 |
| Summary: | 碩士 === 靜宜大學 === 資訊管理學系研究所 === 90 === The longest common subsequence (LCS) problem is a famous NP-Hard problem, which is to find the longest common subsequence on a set S of n strings of length m over an alphabet setΣ. This problem has many important applications in different areas. One important application in molecular biology is to measure the similarity of biological sequences.
In this thesis, we propose two new approximation algorithms MSTG and the AS-LCS for LCS problem. MSTG and AS-LCS have time complexity O(nm4logm) and O(nm4logm + R ∙ l ∙ n ∙ m2) respectively, where R is the user-defined number of iteration and l is the number of ants. MSTG is a greedy algorithm based on a minimal spanning tree. And AS-LCS applies the Ant Colony Optimization (ACO) algorithm to the LCS problem by the idea derived from the traveling salesman problem (TSP). We considered more about the common areas between each pair of sequences in the given set and the use of special merging strategies to get a longer LCS. We also have provided that MSTG and AS-LCS all have performance ratios |Σ| and from the experimental results in DNA and protein sequences, we have proved that both of the two proposed algorithms indeed are superior than the previous algorithms.
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