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We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]),…

Formal Languages and Automata Theory · Computer Science 2026-05-11 Antoine Amarilli , Sebastien Labbe , Charles Paperman

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

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 study the following substring suffix selection problem: given a substring of a string T of length n, compute its k-th lexicographically smallest suffix. This a natural generalization of the well-known question of computing the maximal…

Data Structures and Algorithms · Computer Science 2013-09-24 Maxim Babenko , Paweł Gawrychowski , Tomasz Kociumaka , Tatiana Starikovskaya

It was recently proved that any SLP generating a given string $w$ can be transformed in linear time into an equivalent balanced SLP of the same asymptotic size. We show that this result also holds for RLSLPs, which are SLPs extended with…

Data Structures and Algorithms · Computer Science 2022-06-28 Gonzalo Navarro , Francisco Olivares , Cristian Urbina

Given $m$ documents of total length $n$, we consider the problem of finding a longest string common to at least $d \geq 2$ of the documents. This problem is known as the \emph{longest common substring (LCS) problem} and has a classic $O(n)$…

Data Structures and Algorithms · Computer Science 2014-07-03 Tomasz Kociumaka , Tatiana Starikovskaya , Hjalte Wedel Vildhøj

Let $w$ be a string of length $n$. The problem of counting factors crossing a position - Problem 64 from the textbook ``125 Problems in Text Algorithms'' [Crochemore, Leqroc, and Rytter, 2021], asks to count the number $\mathcal{C}(w,k)$…

Data Structures and Algorithms · Computer Science 2025-07-01 Haruki Umezaki , Hiroki Shibata , Dominik Köppl , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai

It is well-known that checking whether a given string $w$ matches a given regular expression $r$ can be done in quadratic time $O(|w|\cdot |r|)$ and that this cannot be improved to a truly subquadratic running time of $O((|w|\cdot…

Data Structures and Algorithms · Computer Science 2025-08-21 Antoine Amarilli , Florin Manea , Tina Ringleb , Markus L. Schmid

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

Given a string $S$ of length $n$, the classic string indexing problem is to preprocess $S$ into a compact data structure that supports efficient subsequent pattern queries. In the \emph{deterministic} variant the goal is to solve the string…

Data Structures and Algorithms · Computer Science 2016-12-07 Philip Bille , Inge Li Gørtz , Frederik Rye Skjoldjensen

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

Data Structures and Algorithms · Computer Science 2007-05-23 L. Allison

We consider the dynamic range minimum problem on the ultra-wide word RAM model of computation. This model extends the classic $w$-bit word RAM model with special ultrawords of length $w^2$ bits that support standard arithmetic and boolean…

Data Structures and Algorithms · Computer Science 2025-03-10 Philip Bille , Inge Li Gørtz , Tord Stordalen , Máximo Pérez López

The rank and select operations over a string of length n from an alphabet of size $\sigma$ have been used widely in the design of succinct data structures. In many applications, the string itself need be maintained dynamically, allowing…

Data Structures and Algorithms · Computer Science 2010-06-25 Meng He , J. Ian Munro

For a string $S$, a palindromic substring $S[i..j]$ is said to be a \emph{shortest unique palindromic substring} ($\mathit{SUPS}$) for an interval $[s, t]$ in $S$, if $S[i..j]$ occurs exactly once in $S$, the interval $[i, j]$ contains $[s,…

Data Structures and Algorithms · Computer Science 2020-03-25 Kiichi Watanabe , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

SMORE (Chen et al., 2023) recently proposed the concept of semantic regular expressions that extend the classical formalism with a primitive to query external oracles such as databases and large language models (LLMs). Such patterns can be…

Programming Languages · Computer Science 2025-04-14 Yifei Huang , Matin Amini , Alexis Le Glaunec , Konstantinos Mamouras , Mukund Raghothaman

We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…

Data Structures and Algorithms · Computer Science 2017-02-07 Yohei Ueki , Diptarama , Masatoshi Kurihara , Yoshiaki Matsuoka , Kazuyuki Narisawa , Ryo Yoshinaka , Hideo Bannai , Shunsuke Inenaga , Ayumi Shinohara

Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time…

Discrete Mathematics · Computer Science 2020-02-05 Nathan Schaar , Vincent Froese , Rolf Niedermeier

We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…

Data Structures and Algorithms · Computer Science 2014-06-06 Philip Bille , Patrick Hagge Cording , Inge Li Gørtz

Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realised by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…

Data Structures and Algorithms · Computer Science 2018-06-08 Panagiotis Charalampopoulos , Maxime Crochemore , Gabriele Fici , Robert Mercas , Solon P. Pissis

Sequence comparison is a prerequisite to virtually all comparative genomic analyses. It is often realized by sequence alignment techniques, which are computationally expensive. This has led to increased research into alignment-free…

Data Structures and Algorithms · Computer Science 2015-12-23 Maxime Crochemore , Gabriele Fici , Robert Mercaş , Solon P. Pissis