Given a string S = {a1, a2, a3, ..., an}, the longest increasing subsequence (LIS) problem is to find a subsequence of the given string such that the subsequence
is increasing and its length is maximal. In a previous result, to find the longest increasing subsequences of each sliding window with a fixed size w of a given string
with length n can be solved in O(w log log n+OUTPUT) time, where O(w log log n+ w^2) time is taken for preprocessing and OUTPUT is the sum of all output lengths. In this thesis, we solve the problem for finding the longest increasing subsequence of every substring of S. With the straightforward implementation of the previous result, the time required for the preprocessing would be O(n^3). We modify the data structure used in the algorithm, hence the required preprocessing time is improved to O(n^2). The time required for the report stage is linear to the size of the output. In other words, our algorithm can find the LIS of every substring in O(n^2+OUTPUT) time. If the LIS's of all substrings are desired to be reported, since there are O(n^2) substrings totally in a given string with length n, our algorithm is optimal.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0827106-160715 |
| Date | 27 August 2006 |
| Creators | Tseng, Chiou-Ting |
| Contributors | Shi-Jinn Horng, Yue-li Wang, Yi-Hsing Chang, Chia-Ping Chen, Chang-Biau Yang |
| 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-0827106-160715 |
| Rights | off_campus_withheld, Copyright information available at source archive |
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