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DOI: 10.4230/LIPIcs.CPM.2022.15
URN: urn:nbn:de:0030-drops-161424
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16142/
Asahiro, Yuichi ; Jansson, Jesper ; Lin, Guohui ; Miyano, Eiji ; Ono, Hirotaka ; Utashima, Tadatoshi
Polynomial-Time Equivalences and Refined Algorithms for Longest Common Subsequence Variants
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Abstract
The problem of computing the longest common subsequence of two sequences (LCS for short) is a classical and fundamental problem in computer science. In this paper, we study four variants of LCS: the Repetition-Bounded Longest Common Subsequence problem (RBLCS) [Yuichi Asahiro et al., 2020], the Multiset-Restricted Common Subsequence problem (MRCS) [Radu Stefan Mincu and Alexandru Popa, 2018], the Two-Side-Filled Longest Common Subsequence problem (2FLCS), and the One-Side-Filled Longest Common Subsequence problem (1FLCS) [Mauro Castelli et al., 2017; Mauro Castelli et al., 2019]. Although the original LCS can be solved in polynomial time, all these four variants are known to be NP-hard. Recently, an exact, O(1.44225ⁿ)-time, dynamic programming (DP)-based algorithm for RBLCS was proposed [Yuichi Asahiro et al., 2020], where the two input sequences have lengths n and poly(n). We first establish that each of MRCS, 1FLCS, and 2FLCS is polynomially equivalent to RBLCS. Then, we design a refined DP-based algorithm for RBLCS that runs in O(1.41422ⁿ) time, which implies that MRCS, 1FLCS, and 2FLCS can also be solved in O(1.41422ⁿ) time. Finally, we give a polynomial-time 2-approximation algorithm for 2FLCS.
BibTeX - Entry
@InProceedings{asahiro_et_al:LIPIcs.CPM.2022.15,
author = {Asahiro, Yuichi and Jansson, Jesper and Lin, Guohui and Miyano, Eiji and Ono, Hirotaka and Utashima, Tadatoshi},
title = {{Polynomial-Time Equivalences and Refined Algorithms for Longest Common Subsequence Variants}},
booktitle = {33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
pages = {15:1--15:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-234-1},
ISSN = {1868-8969},
year = {2022},
volume = {223},
editor = {Bannai, Hideo and Holub, Jan},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16142},
URN = {urn:nbn:de:0030-drops-161424},
doi = {10.4230/LIPIcs.CPM.2022.15},
annote = {Keywords: Repetition-bounded longest common subsequence problem, multiset restricted longest common subsequence problem, one-side-filled longest common subsequence problem, two-side-filled longest common subsequence problem, exact algorithms, and approximation algorithms}
}
| Keywords: | Repetition-bounded longest common subsequence problem, multiset restricted longest common subsequence problem, one-side-filled longest common subsequence problem, two-side-filled longest common subsequence problem, exact algorithms, and approximation algorithms | |
| Seminar: | 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022) | |
| Issue date: | 2022 | |
| Date of publication: | 22.06.2022 |
