Faster Algorithms for Computing Longest Common Increasing Subsequences

Brodal, Gerth Stølting; Kaligosi, Kanela; Katriel, Irit; Kutz, Martin

doi:10.1007/11780441_30

Cited by 13 publications

(5 citation statements)

References 13 publications

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“…Deorowicz's algorithm is more efficient when the alphabet size increases. Iliopoulos and Rahman [16] proposed an algorithm in O(rR log log n + n) time by using the DP formula of Arslan and Egecioglu [2] and the bounded heap (BH) data structure [4]. Deorowicz and Obstój [9] proposed an algorithm in O(r(mL + R) + n) time based on the entry-exit point approach [10].…”

Section: Introductionmentioning

confidence: 99%

A Diagonal-Based Algorithm for the Constrained Longest Common Subsequence Problem

Hung

Yang

Huang

2019

Communications in Computer and Information Science

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The longest common subsequence (LCS) problem and its variations have been studied deeply in past decades. In the constrained longest common subsequence (CLCS) problem, given three sequences A, B, and C of lengths m, n, and r, respectively, its goal is to find the LCS of A and B that C is a subsequence contained in the LCS answer. This thesis proposes an algorithm for obtaining the CLCS length based on the diagonal concept for finding the LCS length proposed by Nakatsu et al. Our algorithm can find the CLCS length more efficiently with O(rL(m − L)) time and O(mr) space, where L is the CLCS length. As the experimental results show, our CLCS algorithm outperforms the previously published algorithms.

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Section: Introductionmentioning

confidence: 99%

A Diagonal-Based Algorithm for the Constrained Longest Common Subsequence Problem

Hung

Yang

Huang

2019

Communications in Computer and Information Science

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“…This method is based on a modification of the dynamic programming formulation from [10]. To perform the matrix calculations of each iteration efficiently, the authors make use of a socalled bounded heap data structure [26] that was realized by means of Van Emde Boas (vEB) trees [27]. This data structure allows to calculate intermediate results more efficiently in O (log log n) time, leading to a total time com-…”

Section: Algorithms Used For Comparisonmentioning

confidence: 99%

An A⁎ search algorithm for the constrained longest common subsequence problem

Djukanovic

Berger²,

Raidl

et al. 2021

Information Processing Letters

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“…The combination of the above two problems is the longest common increasing subsequence problem, i.e., the problem of computing the longest common subsequence that is also an increasing subsequence of the given strings. Some important works on this problem are (Yang et al, 2005; Brodal et al, 2006). …”

Section: Related Problemsmentioning

confidence: 99%

Near-optimal algorithm to count occurrences of subsequences of a given length

Torres-Jiménez

Izquierdo-Marquez

Ramirez-Acuna

et al. 2017

Discrete Math. Algorithm. Appl.

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For k ∈ ℤ+, define Σk as the set of integers {0, 1, …, k − 1}. Given an integer n and a string t of length m ≥ n over Σk, we count the number of times that each one of the kn distinct strings of length n over Σk occurs as a subsequence of t. Our algorithm makes only one scan of t and solves the problem in time complexity mkn−1 and space complexity m + kn. These are very close to best possible.

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Faster Algorithms for Computing Longest Common Increasing Subsequences

Cited by 13 publications

References 13 publications

A Diagonal-Based Algorithm for the Constrained Longest Common Subsequence Problem

A Diagonal-Based Algorithm for the Constrained Longest Common Subsequence Problem

An A⁎ search algorithm for the constrained longest common subsequence problem

Near-optimal algorithm to count occurrences of subsequences of a given length

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