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DOI: 10.4230/LIPIcs.STACS.2020.41
URN: urn:nbn:de:0030-drops-119020
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11902/
Duraj, Lech
A Sub-Quadratic Algorithm for the Longest Common Increasing Subsequence Problem
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Abstract
The Longest Common Increasing Subsequence problem (LCIS) is a natural variant of the celebrated Longest Common Subsequence (LCS) problem. For LCIS, as well as for LCS, there is an 𝒪(n²)-time algorithm and a SETH-based conditional lower bound of 𝒪(n^{2-ε}). For LCS, there is also the Masek-Paterson 𝒪(n²/log n)-time algorithm, which does not seem to adapt to LCIS in any obvious way. Hence, a natural question arises: does any (slightly) sub-quadratic algorithm exist for the Longest Common Increasing Subsequence problem? We answer this question positively, presenting a 𝒪(n²/log^a n)-time algorithm for a = 1/6-o(1). The algorithm is not based on memorizing small chunks of data (often used for logarithmic speedups, including the "Four Russians Trick" in LCS), but rather utilizes a new technique, bounding the number of significant symbol matches between the two sequences.
BibTeX - Entry
@InProceedings{duraj:LIPIcs:2020:11902,
author = {Lech Duraj},
title = {{A Sub-Quadratic Algorithm for the Longest Common Increasing Subsequence Problem}},
booktitle = {37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
pages = {41:1--41:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-140-5},
ISSN = {1868-8969},
year = {2020},
volume = {154},
editor = {Christophe Paul and Markus Bl{\"a}ser},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/11902},
URN = {urn:nbn:de:0030-drops-119020},
doi = {10.4230/LIPIcs.STACS.2020.41},
annote = {Keywords: longest common increasing subsequence, log-shaving, matching pairs}
}
| Keywords: | longest common increasing subsequence, log-shaving, matching pairs | |
| Seminar: | 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.03.2020 |
