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In the Longest Common Factor with $k$ Mismatches (LCF$_k$) problem, we are given two strings $X$ and $Y$ of total length $n$, and we are asked to find a pair of maximal-length factors, one of $X$ and the other of $Y$, such that their…

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

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

The Longest Common Subsequence (LCS) is the problem of finding a subsequence among a set of strings that has two properties of being common to all and is the longest. The LCS has applications in computational biology and text editing, among…

Artificial Intelligence · Computer Science 2023-06-07 Alireza Abdi , Masih Hajsaeedi , Mohsen Hooshmand

Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is…

Data Structures and Algorithms · Computer Science 2023-06-21 Kazuki Mitani , Takuya Mieno , Kazuhisa Seto , Takashi Horiyama

At CPM 2017, Castelli et al. define and study a new variant of the Longest Common Subsequence Problem, termed the Longest Filled Common Subsequence Problem (LFCS). For the LFCS problem, the input consists of two strings $A$ and $B$ and a…

Data Structures and Algorithms · Computer Science 2019-08-06 Radu Stefan Mincu , Alexandru Popa

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

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

Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length of the longest palindromic substrings (LPSs) of a given string…

Data Structures and Algorithms · Computer Science 2021-01-11 Mitsuru Funakoshi , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings $S$…

Data Structures and Algorithms · Computer Science 2026-04-09 Panagiotis Charalampopoulos , Paweł Gawrychowski , Karol Pokorski

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

We consider the canonical generalization of the well-studied Longest Increasing Subsequence problem to multiple sequences, called $k$-LCIS: Given $k$ integer sequences $X_1,\dots,X_k$ of length at most $n$, the task is to determine the…

Computational Complexity · Computer Science 2020-04-10 Lech Duraj , Marvin Künnemann , Adam Polak

Let $X_1, X_2, ..., X_s$ and $Y_1, Y_2, ..., Y_t$ be strings over an alphabet $\Sigma$, where $s$ and $t$ are positive integers. The longest common subsequence and substring problem for multiple strings $X_1, X_2, ..., X_s$ and $Y_1, Y_2,…

Data Structures and Algorithms · Computer Science 2024-11-26 Rao Li

We present an algorithm computing the longest periodic subsequence of a string of length $n$ in $O(n^7)$ time with $O(n^4)$ words of space. We obtain improvements when restricting the exponents or extending the search allowing the reported…

Data Structures and Algorithms · Computer Science 2022-02-16 Hideo Bannai , Tomohiro I , Dominik Köppl

In this paper we initiate the study of computing a maximal (not necessarily maximum) repeating pattern in a single input string, where the corresponding problems have been studied (e.g., a maximal common subsequence) only in two or more…

Data Structures and Algorithms · Computer Science 2026-01-21 Mingyang Gong , Adiesha Liyanage , Braeden Sopp , Binhai Zhu

In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…

Quantum Physics · Physics 2024-04-05 Kamil Khadiev , Carlos Manuel Bosch Machado , Zeyu Chen , Junde Wu

The Longest Common Subsequence (LCS) problem is a fundamental problem of sequence comparison. A natural approximation to this problem is a model in which every pairs of letters of two ``sequences'' are matched independently of the other…

Disordered Systems and Neural Networks · Physics 2016-08-31 J. Boutet de Monvel

Maximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which…

Data Structures and Algorithms · Computer Science 2023-07-26 Alessio Conte , Roberto Grossi , Giulia Punzi , Takeaki Uno

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

We give a near-optimal quantum algorithm for the longest common substring (LCS) problem between two run-length encoded (RLE) strings, with the assumption that the prefix-sums of the run-lengths are given. Our algorithm costs…

Quantum Physics · Physics 2024-11-06 Tzu-Ching Lee , Han-Hsuan Lin