Longest Common Subsequence on Weighted Sequences.
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Documents
- 1901.04068-pre-print
Submitted manuscript, 250 KB, PDF document
- 1901.04068-post-print
Accepted author manuscript, 540 KB, PDF document
- LIPIcs-CPM-2020-19
Final published version, 475 KB, PDF document
We consider the general problem of the Longest Common Subsequence (LCS) on weighted sequences. Weighted sequences are an extension of classical strings, where in each position every letter of the alphabet may occur with some probability. Previous results presented a PTAS and noticed that no FPTAS is possible unless P=NP. In this paper we essentially close the gap between upper and lower bounds by improving both. First of all, we provide an EPTAS for bounded alphabets (which is the most natural case), and prove that there does not exist any EPTAS for unbounded alphabets unless FPT=W[1]. Furthermore, under the Exponential Time Hypothesis, we provide a lower bound which shows that no significantly better PTAS can exist for unbounded alphabets. As a side note, we prove that it is sufficient to work with only one threshold in the general variant of the problem.
Original language | English |
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Title of host publication | Longest Common Subsequence on Weighted Sequences. |
Number of pages | 15 |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Publication date | Jun 2020 |
ISBN (Print) | 978-3-95977-149-8 |
DOIs | |
Publication status | Published - Jun 2020 |
Externally published | Yes |
Series | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 161 |
ISSN | 1868-8969 |
Bibliographical note
Received the Alberto Apostolico Best Paper Award.
Links
- https://arxiv.org/abs/1901.04068
Submitted manuscript
- https://arxiv.org/abs/1901.04068
Accepted author manuscript
- https://drops.dagstuhl.de/opus/volltexte/2020/12144/
Final published version
ID: 257869307