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Polynomial-Time Equivalences and Refined Algorithms for Longest Common Subsequence Variants

Authors Yuichi Asahiro, Jesper Jansson, Guohui Lin, Eiji Miyano, Hirotaka Ono, Tadatoshi Utashima

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Document Identifiers

Author Details

Yuichi Asahiro
  • Kyushu Sangyo University, Fukuoka, Japan
Jesper Jansson
  • Kyoto University, Japan
Guohui Lin
  • University of Alberta, Edmonton, Canada
Eiji Miyano
  • Kyushu Institute of Technology, Iizuka, Japan
Hirotaka Ono
  • Nagoya University, Japan
Tadatoshi Utashima
  • Kyushu Institute of Technology, Iizuka, Japan

Funding

This work is partially supported by NSERC Canada, JST CREST JPMJR1402, and JSPS KAKENHI Grant Numbers JP20H05967, JP21K11755, JP21K19765, JP22H00513, and JP22K11915.

Cite As Get BibTex

Yuichi Asahiro, Jesper Jansson, Guohui Lin, Eiji Miyano, Hirotaka Ono, and Tadatoshi Utashima. Polynomial-Time Equivalences and Refined Algorithms for Longest Common Subsequence Variants. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CPM.2022.15

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of 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

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References

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