Various approaches have been proposed for finding the longest
common subsequence (LCS) of two sequences. The time complexities
of these algorithms are usually $O(n^2)$ in the worst case, where
$n$ is the length of input sequences. However, these algorithms
would become infeasible when the input length, $n$, is very long.
Recently, the $k$-LCS $(k ≥ 2)$ problem has become more
attractive. Some algorithms have been proposed for solving the
problem, but the execution time required for solving the $k$-LCS
problem is still too long to be practical. In this thesis, we
propose a genetic algorithm for solving the $k$-LCS problem with
time complexity $O(Gpk(n + |P_j|))$, which $G$ is the number of
generations, $p$ is the number of template patterns, $k$ is the
number of input sequences, $n$ and $|P_j|$ are the length of input
sequences and the length of template patterns, respectively. As
our experimental results show, when $k$ is 20 and $n$ is 1000, the
performance ratio ($|CS|/|LCS|$) of our algorithm is greater than
0.8, where $|CS|$ denotes the length of the solution we find, and
$|LCS|$ represents the length of the real (optimal) LCS. Comparing
the performance ratios with Expansion Algorithm and BNMAS
Algorithm, our algorithm is much better than them when the number
of input sequences varies from 2 to 20 and the length of the input
sequences varies from 100 to 2000.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0106109-080018 |
| Date | 06 January 2009 |
| Creators | Chiang, Chung-Han |
| Contributors | none, Chang-Biau Yang, none, none, none |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0106109-080018 |
| Rights | off_campus_withheld, Copyright information available at source archive |
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