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Finding the common subsequences of $L$ multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well-known result states that finding a Longest Common Subsequence (LCS)…

Data Structures and Algorithms · Computer Science 2020-09-09 Jin Cao , Dewei Zhong

Longest common subsequence (LCS) is one of the most fundamental problems in combinatorial optimization. Apart from theoretical importance, LCS has enormous applications in bioinformatics, revision control systems, and data comparison…

Data Structures and Algorithms · Computer Science 2020-03-17 MohammadTaghi Hajiaghayi , Masoud Seddighin , Saeed Seddighin , Xiaorui Sun

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

Data Structures and Algorithms · Computer Science 2022-07-01 Anas Al-okaily , Abdelghani Tbakhi

Given a text and a pattern over an alphabet, the pattern matching problem searches for all occurrences of the pattern in the text. An equivalence relation $\approx$ is called a substring consistent equivalence relation (SCER), if for two…

Data Structures and Algorithms · Computer Science 2022-07-28 Davaajav Jargalsaikhan , Diptarama Hendrian , Ryo Yoshinaka , Ayumi Shinohara

Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of…

Computational Complexity · Computer Science 2015-02-02 Amir Abboud , Arturs Backurs , Virginia Vassilevska Williams

A classical measure of string comparison is given by the longest common subsequence (LCS) problem on a pair of strings. We consider its generalisation, called the semi-local LCS problem, which arises naturally in many string-related…

Data Structures and Algorithms · Computer Science 2015-03-13 Alexander Tiskin

The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…

Data Structures and Algorithms · Computer Science 2021-11-10 Moses Ganardi , Paweł Gawrychowski

The Longest Common Increasing Subsequence problem (LCIS) is a natural variant of the celebrated Longest Common Subsequence (LCS) problem. For LCIS, as well as for LCS, there is an $O(n^2)$-time algorithm and a SETH-based conditional lower…

Data Structures and Algorithms · Computer Science 2020-01-31 Lech Duraj

Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation graphs…

Computational Complexity · Computer Science 2020-06-04 Massimo Equi , Roberto Grossi , Veli Mäkinen

The problem of finding longest common subsequence (LCS) is one of the fundamental problems in computer science, which finds application in fields such as computational biology, text processing, information retrieval, data compression etc.…

Computational Complexity · Computer Science 2020-06-25 Amey Bhangale , Diptarka Chakraborty , Rajendra Kumar

Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…

Data Structures and Algorithms · Computer Science 2011-11-10 Alexander Tiskin

The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE…

Data Structures and Algorithms · Computer Science 2015-07-10 Philip Bille , Pawel Gawrychowski , Inge Li Goertz , Gad M. Landau , Oren Weimann

The constrained LCS problem asks one to find a longest common subsequence of two input strings $A$ and $B$ with some constraints. The STR-IC-LCS problem is a variant of the constrained LCS problem, where the solution must include a given…

Data Structures and Algorithms · Computer Science 2017-03-16 Keita Kuboi , Yuta Fujishige , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

The Cover Suffix Tree (CST) of a string $T$ is the suffix tree of $T$ with additional explicit nodes corresponding to halves of square substrings of $T$. In the CST an explicit node corresponding to a substring $C$ of $T$ is annotated with…

Data Structures and Algorithms · Computer Science 2023-08-09 Jakub Radoszewski

The recently introduced longest common substring with $k$-mismatches ($k$-LCF) problem is to find, given two sequences $S_1$ and $S_2$ of length $n$ each, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance…

Data Structures and Algorithms · Computer Science 2014-10-15 Szymon Grabowski

Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…

Data Structures and Algorithms · Computer Science 2023-11-10 Tomasz Kociumaka , Gonzalo Navarro , Francisco Olivares

In this paper, we consider a generalized longest common subsequence problem, in which a constraining sequence of length $s$ must be included as a substring and the other constraining sequence of length $t$ must be excluded as a subsequence…

Data Structures and Algorithms · Computer Science 2015-06-02 Daxin Zhu , Lei Wang , Yingjie Wu , Xiaodong Wang

Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the string matching problem is a task to find all occurrences of $P$ in $T$. In this study, we propose an algorithm that solves this problem in $O((n + m)q)$ time considering…

Data Structures and Algorithms · Computer Science 2020-04-14 Satoshi Kobayashi , Diptarama Hendrian , Ryo Yoshinaka , Ayumi Shinohara

Given two strings $S$ and $P$, the Episode Matching problem is to find the shortest substring of $S$ that contains $P$ as a subsequence. The best known upper bound for this problem is $\tilde O(nm)$ by Das et al. (1997) , where $n,m$ are…

Data Structures and Algorithms · Computer Science 2024-02-15 Philip Bille , Inge Li Gørtz , Shay Mozes , Teresa Anna Steiner , Oren Weimann

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