Polynomial-time equivalences and refined algorithms for longest common subsequence variants

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 article, we study four variants of LCS: the Repetition-Bounded Longest Common Subsequence problem (RBLCS), the Multiset-Restricted Common Subse...

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Vydané v:Discrete Applied Mathematics Ročník 353; s. 44 - 64
Hlavní autori: Asahiro, Yuichi, Jansson, Jesper, Lin, Guohui, Miyano, Eiji, Ono, Hirotaka, Utashima, Tadatoshi
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 15.08.2024
Predmet:
Approximation algorithm
Dynamic programming
Exact algorithm
Longest common subsequence
Multiset-restricted
One-side-filled
Repetition-bounded
Two-side-filled
Multiset-restricted
Longest common subsequence
Two-side-filled
Dynamic programming
Exact algorithm
Approximation algorithm
One-side-filled
Repetition-bounded
ISSN:0166-218X, 1872-6771
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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 article, we study four variants of LCS: the Repetition-Bounded Longest Common Subsequence problem (RBLCS), the Multiset-Restricted Common Subsequence problem (MRCS), the Two-Side-Filled Longest Common Subsequence problem (2FLCS), and the One-Side-Filled Longest Common Subsequence problem (1FLCS). 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, where the two input sequences have lengths n and poly(n). Here, 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.
AbstractList 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 article, we study four variants of LCS: the Repetition-Bounded Longest Common Subsequence problem (RBLCS), the Multiset-Restricted Common Subsequence problem (MRCS), the Two-Side-Filled Longest Common Subsequence problem (2FLCS), and the One-Side-Filled Longest Common Subsequence problem (1FLCS). 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, where the two input sequences have lengths n and poly(n). Here, 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.
Author Utashima, Tadatoshi
Miyano, Eiji
Asahiro, Yuichi
Lin, Guohui
Jansson, Jesper
Ono, Hirotaka
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10.1016/j.tcs.2020.07.042
10.1145/321796.321811
10.1186/1471-2105-11-304
10.1145/360825.360861
10.1145/321879.321880
10.1109/TCBB.2012.57
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Keywords Multiset-restricted
Longest common subsequence
Two-side-filled
Dynamic programming
Exact algorithm
Approximation algorithm
One-side-filled
Repetition-bounded
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SubjectTerms Approximation algorithm
Dynamic programming
Exact algorithm
Longest common subsequence
Multiset-restricted
One-side-filled
Repetition-bounded
Two-side-filled
Title Polynomial-time equivalences and refined algorithms for longest common subsequence variants
URI https://dx.doi.org/10.1016/j.dam.2024.04.006
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