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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

Given a set of $k$ strings $I$, their longest common subsequence (LCS) is the string with the maximum length that is a subset of all the strings in $I$. A data-structure for this problem preprocesses $I$ into a data-structure such that the…

Data Structures and Algorithms · Computer Science 2021-01-13 Sepideh Aghamolaei

The longest common substring with $k$-mismatches problem is to find, given two strings $S_1$ and $S_2$, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ and $A_2$ is $\le k$. We introduce a…

Data Structures and Algorithms · Computer Science 2015-04-08 Tomas Flouri , Emanuele Giaquinta , Kassian Kobert , Esko Ukkonen

We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…

Data Structures and Algorithms · Computer Science 2021-10-22 Shyan Akmal , Ce Jin

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

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

Chaining algorithms aim to form a semi-global alignment of two sequences based on a set of anchoring local alignments as input. Depending on the optimization criteria and the exact definition of a chain, there are several $O(n \log n)$ time…

Data Structures and Algorithms · Computer Science 2020-04-27 Veli Mäkinen , Kristoffer Sahlin

In this paper we present algorithms for several string problems in the Congested Clique model. In the Congested Clique model, $n$ nodes (computers) are used to solve some problem. The input to the problem is distributed among the nodes, and…

Data Structures and Algorithms · Computer Science 2025-04-14 Shay Golan , Matan Kraus

The Longest Common Subsequence (LCS) of two strings is a fundamental string similarity measure with a classical dynamic programming solution taking quadratic time. Despite significant efforts, little progress was made in improving the…

Data Structures and Algorithms · Computer Science 2021-12-17 Negev Shekel Nosatzki

This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…

Discrete Mathematics · Computer Science 2007-05-23 Ronald I. Greenberg

In the classic longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, over an alphabet of size $\sigma$, and we are asked to find a longest string occurring as a fragment of both $S$ and…

Data Structures and Algorithms · Computer Science 2025-11-18 Panagiotis Charalampopoulos , Tomasz Kociumaka , Jakub Radoszewski , Solon P. Pissis

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,…

In this paper, we consider the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). The problem is as follows. For a positive integer $n$, a sequence of n strings $S=(s^1,\dots,s^n)$ is given. We should…

Quantum Physics · Physics 2021-12-28 Kamil Khadiev , Carlos Manuel Bosch Machado

The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…

Data Structures and Algorithms · Computer Science 2023-04-04 Paweł Gawrychowski , Garance Gourdel , Tatiana Starikovskaya , Teresa Anna Steiner

Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…

Data Structures and Algorithms · Computer Science 2025-04-08 Giovanni Buzzega , Alessio Conte , Yasuaki Kobayashi , Kazuhiro Kurita , Giulia Punzi

The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…

Data Structures and Algorithms · Computer Science 2008-07-29 Dimitris Papamichail , Georgios Papamichail

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

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

We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…

Quantum Physics · Physics 2020-01-08 Kamil Khadiev , Artem Ilikaev

Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…

Data Structures and Algorithms · Computer Science 2025-09-22 Hamed Hasibi , Neerja Mhaskar , W. F. Smyth