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The longest common extension problem is to preprocess a given string of length $n$ into a data structure that uses $S(n)$ bits on top of the input and answers in $T(n)$ time the queries $\mathit{LCE}(i,j)$ computing the length of the…

Data Structures and Algorithms · Computer Science 2017-05-12 Dmitry Kosolobov

The circuit-level implementation of a quantum string-matching algorithm, which matches a search string (pattern) of length $M$ inside a longer text of length $N$, has already been demonstrated in the literature to outperform its classical…

Quantum Physics · Physics 2023-04-07 Amit Saha , Om Khanna

Determining whether an unordered collection of overlapping substrings (called shingles) can be uniquely decoded into a consistent string is a problem that lies within the foundation of a broad assortment of disciplines ranging from…

Discrete Mathematics · Computer Science 2012-04-17 Aryeh Kontorovich , Ari Trachtenberg

Given strings $P$ and $Q$ the (exact) string matching problem is to find all positions of substrings in $Q$ matching $P$. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time…

Data Structures and Algorithms · Computer Science 2010-09-08 Philip Bille

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

Repeat finding in strings has important applications in subfields such as computational biology. The challenge of finding the longest repeats covering particular string positions was recently proposed and solved by \.{I}leri et al., using a…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-01-28 Yun Tian , Bojian Xu

We study the problem of aligning multiple sequences with the goal of finding an alignment that either maximizes the number of aligned symbols (the longest common subsequence (LCS)), or minimizes the number of unaligned symbols (the…

Data Structures and Algorithms · Computer Science 2021-10-26 Debarati Das , Barna Saha

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

There is a large literature devoted to the problem of finding an optimal (min-cost) prefix-free code with an unequal letter-cost encoding alphabet of size. While there is no known polynomial time algorithm for solving it optimally there are…

Information Theory · Computer Science 2007-07-13 Mordecai Golin , Li Jian

We consider the communication complexity of fundamental longest common prefix (Lcp) problems. In the simplest version, two parties, Alice and Bob, each hold a string, $A$ and $B$, and we want to determine the length of their longest common…

Data Structures and Algorithms · Computer Science 2018-06-11 Philip Bille , Mikko Berggreen Ettienne , Roberto Grossi , Inge Li Gørtz , Eva Rotenberg

We consider computing the longest palindrome in a text of length $n$ in the streaming model, where the characters arrive one-by-one, and we do not have random access to the input. While computing the answer exactly using sublinear memory is…

Data Structures and Algorithms · Computer Science 2016-04-08 Paweł Gawrychowski , Przemysław Uznański

In this work, we present a plethora of results for the range longest increasing subsequence problem (Range-LIS) and its variants. The input to RLIS is a sequence $S$ of $n$ real numbers and a collection $Q$ of $m$ query ranges, and for each…

Data Structures and Algorithms · Computer Science 2025-12-02 Karthik C. S. , Saladi Rahul

The normalized substring complexity $\delta$ of a string is defined as $\max_k \{c[k]/k\}$, where $c[k]$ is the number of \textit{distinct} substrings of length $k$. This simply defined measure has recently attracted attention due to its…

Data Structures and Algorithms · Computer Science 2026-02-17 Gregory Kucherov , Yakov Nekrich

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

In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…

Data Structures and Algorithms · Computer Science 2016-04-11 Paweł Gawrychowski , Adam Karczmarz , Tomasz Kociumaka , Jakub Łącki , Piotr Sankowski

Let two static sequences of strings $P$ and $S$, representing prefix and suffix conditions respectively, be given as input for preprocessing. For the query, let two positive integers $k_1$ and $k_2$ be given, as well as a string $T$ given…

Data Structures and Algorithms · Computer Science 2022-11-01 Laurentius Leonard , Shunsuke Inenaga , Hideo Bannai , Takuya Mieno

We consider the problem of finding repetitive structures and inherent patterns in a given string $\s{s}$ of length $n$ over a finite totally ordered alphabet. A border $\s{u}$ of a string $\s{s}$ is both a prefix and a suffix of $\s{s}$…

Data Structures and Algorithms · Computer Science 2015-06-24 Ali Alatabbi , Jacqueline W. Daykin , M. Sohel Rahman

Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…

Quantum Physics · Physics 2024-04-01 Zeguan Wu , Sidhant Misra , Tamás Terlaky , Xiu Yang , Marc Vuffray

We consider the Abelian longest common factor problem in two scenarios: when input strings are uncompressed and are of size $n$, and when the input strings are run-length encoded and their compressed representations have size at most $m$.…

Data Structures and Algorithms · Computer Science 2018-04-19 Szymon Grabowski , Tomasz Kociumaka , Jakub Radoszewski

In this paper, we propose a data structure, a quadruple neighbor list (QN-list, for short), to support real time queries of all longest increasing subsequence (LIS) and LIS with constraints over sequential data streams. The QN-List built by…

Data Structures and Algorithms · Computer Science 2016-10-12 Youhuan Li , Lei Zou , Huaming Zhang , Dongyan Zhao