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Longest Common Substring (LCS) is an important text processing problem, which has recently been investigated in the quantum query model. The decisional version of this problem, LCS with threshold $d$, asks whether two length-$n$ input…

Data Structures and Algorithms · Computer Science 2022-11-30 Ce Jin , Jakob Nogler

Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…

Quantum Physics · Physics 2023-12-29 François Le Gall , Saeed Seddighin

Two strings of the same length are said to Cartesian-tree match (CT-match) if their Cartesian-trees are isomorphic [Park et al., TCS 2020]. Cartesian-tree matching is a natural model that allows for capturing similarities of numerical…

Data Structures and Algorithms · Computer Science 2026-01-01 Taketo Tsujimoto , Yuki Yonemoto , Hiroki Shibata , Takuya Mieno , Yuto Nakashima , Shunsuke Inenaga

In this paper we present $LCSk$++: a new metric for measuring the similarity of long strings, and provide an algorithm for its efficient computation. With ever increasing size of strings occuring in practice, e.g. large genomes of plants…

Data Structures and Algorithms · Computer Science 2019-08-27 Filip Pavetić , Goran Žužić , Mile Šikić

The Longest Common Subsequence (LCS) problem is a very important problem in math- ematics, which has a broad application in scheduling problems, physics and bioinformatics. It is known that the given two random sequences of infinite…

Discrete Mathematics · Computer Science 2013-06-19 Kang Ning , Kwok Pui Choi

Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…

Data Structures and Algorithms · Computer Science 2021-11-23 Aviad Rubinstein , Saeed Seddighin , Zhao Song , Xiaorui Sun

In this paper we address the constrained longest common subsequence problem. Given two sequences $X$, $Y$ and a constrained sequence $P$, a sequence $Z$ is a constrained longest common subsequence for $X$ and $Y$ with respect to $P$ if $Z$…

Data Structures and Algorithms · Computer Science 2021-03-05 Francis Yuk Lun Chin , Ngai Lam Ho , Alfredo De Santis , S. K. Kim

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently…

Data Structures and Algorithms · Computer Science 2018-05-02 Tristan Braquelaire , Marie Gasparoux , Mathieu Raffinot , Raluca Uricaru

This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common…

Data Structures and Algorithms · Computer Science 2016-08-26 Daxin Zhu , Lei Wang , Tinran Wang , Xiaodong Wang

A weighted string, also known as a position weight matrix, is a sequence of probability distributions over some alphabet. We revisit the Weighted Shortest Common Supersequence (WSCS) problem, introduced by Amir et al. [SPIRE 2011], that is,…

We present the first $\mathrm{o}(n)$-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length $n$, the algorithm runs in $\mathrm{O}(n^{3})$ time with $\mathrm{O}\left(\frac{n…

Data Structures and Algorithms · Computer Science 2020-09-21 Masashi Kiyomi , Takashi Horiyama , Yota Otachi

A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…

Data Structures and Algorithms · Computer Science 2026-04-15 Daniel Albert

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…

Data Structures and Algorithms · Computer Science 2017-12-27 Masashi Kiyomi , Hirotaka Ono , Yota Otachi , Pascal Schweitzer , Jun Tarui

This paper shows that a simple algorithm produces the {\em all-prefixes-LCSs-graph} in $O(mn)$ time for two input sequences of size $m$ and $n$. Given any prefix $p$ of the first input sequence and any prefix $q$ of the second input…

Data Structures and Algorithms · Computer Science 2011-03-09 Ronald I. Greenberg

This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.

Data Structures and Algorithms · Computer Science 2007-05-23 Ronald I. Greenberg

We present a practical algorithm for the cyclic longest common subsequence (CLCS) problem that runs in O(mn) time, where m and n are the lengths of the two input strings. While this is not necessarily an asymptotic improvement over the…

Data Structures and Algorithms · Computer Science 2012-08-17 Andy Nguyen

We give a sublinear quantum algorithm for the longest common substring (LCS) problem on the run-length encoded (RLE) inputs, under the assumption that the prefix-sums of the runs are given. Our algorithm costs $\tilde{O}(n^{5/6})\cdot…

Quantum Physics · Physics 2023-10-03 Tzu-Ching Lee , Han-Hsuan Lin

Motivated by computing duplication patterns in sequences, a new fundamental problem called the longest subsequence-repeated subsequence (LSRS) is proposed. Given a sequence $S$ of length $n$, a letter-repeated subsequence is a subsequence…

Data Structures and Algorithms · Computer Science 2023-09-01 Manuel Lafond , Wenfeng Lai , Adiesha Liyanage , Binhai Zhu

The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical…

Data Structures and Algorithms · Computer Science 2023-09-06 Domenico Cantone , Simone Faro , Arianna Pavone , Caterina Viola

Let $\Sigma$ be an alphabet. For two strings $X$, $Y$, and a constrained string $P$ over the alphabet $\Sigma$, the constrained longest common subsequence and substring problem for two strings $X$ and $Y$ with respect to $P$ is to find a…

Data Structures and Algorithms · Computer Science 2023-08-04 R. Li , J. Deka , K. Deka , D. Li