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We consider compact representations of collections of similar strings that support random access queries. The collection of strings is given by a rooted tree where edges are labeled by an edit operation (inserting, deleting, or replacing a…

数据结构与算法 · 计算机科学 2021-02-12 Philip Bille , Inge Li Gørtz

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 $O(n)$…

数据结构与算法 · 计算机科学 2014-07-03 Tomasz Kociumaka , Tatiana Starikovskaya , Hjalte Wedel Vildhøj

The {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. Palindrome is a word which reads the same forward as it does backward. The {\em longest common palindromic subsequence (LCPS)}…

数据结构与算法 · 计算机科学 2011-10-25 Shihabur Rahman Chowdhury , Md. Mahbubul Hasan , Sumaiya Iqbal , M. Sohel Rahman

Given strings $P$ of length $m$ and $T$ of length $n$ over an alphabet of size $\sigma$, the string matching with $k$-mismatches problem is to find the positions of all the substrings in $T$ that are at Hamming distance at most $k$ from…

数据结构与算法 · 计算机科学 2013-08-01 Emanuele Giaquinta , Szymon Grabowski , Kimmo Fredriksson

We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text $T[1..u]$ that is represented by a (context-free) grammar of…

数据结构与算法 · 计算机科学 2011-10-21 Francisco Claude , Gonzalo Navarro

We show that the compressed suffix array and the compressed suffix tree for a string of length $n$ over an integer alphabet of size $\sigma\leq n$ can both be built in $O(n)$ (randomized) time using only $O(n\log\sigma)$ bits of working…

数据结构与算法 · 计算机科学 2016-05-24 Djamal Belazzougui

It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. But is it possible to construct a few strings, not longer than the input string, so that most of them have larger complexity? We show that the…

计算复杂性 · 计算机科学 2017-02-07 Marius Zimand

In this paper, we consider a generalized longest common subsequence problem with multiple substring inclusive constraints. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constraints $P=\{P_1,\cdots,P_d\}$…

数据结构与算法 · 计算机科学 2015-05-26 Daxin Zhu , Lei Wang , Yingjie Wu , Xiaodong Wang

Two strings are considered to have parameterized matching when there exists a bijection of the parameterized alphabet onto itself such that it transforms one string to another. Parameterized matching has application in software duplication…

数据结构与算法 · 计算机科学 2024-12-03 Apurba Saha , Iftekhar Hakim Kaowsar , Mahdi Hasnat Siyam , M. Sohel Rahman

Lempel-Ziv (LZ77) factorization is a fundamental problem in string processing: Greedily partition a given string $T$ from left to right into blocks (called phrases) so that each phrase is either the leftmost occurrence of a letter or the…

数据结构与算法 · 计算机科学 2025-06-19 Dominik Kempa , Tomasz Kociumaka

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…

数据结构与算法 · 计算机科学 2016-04-11 Paweł Gawrychowski , Adam Karczmarz , Tomasz Kociumaka , Jakub Łącki , Piotr Sankowski

We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…

分布式、并行与集群计算 · 计算机科学 2015-07-14 Y. Métivier , J. M. Robson , A. Zemmari

We revisit the problem of longest common property preserving substring queries introduced by~Ayad et al. (SPIRE 2018, arXiv 2018). We consider a generalized and unified on-line setting, where we are given a set $X$ of $k$ strings of total…

数据结构与算法 · 计算机科学 2019-06-14 Kazuki Kai , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda , Tomasz Kociumaka

Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…

离散数学 · 计算机科学 2014-03-12 Jayadev Acharya , Hirakendu Das , Olgica Milenkovic , Alon Orlitsky , Shengjun Pan

We study the following rearrangement problem: Given $n$ words, rearrange and concatenate them so that the obtained string is lexicographically smallest (or largest, respectively). We show that this problem reduces to sorting the given words…

数据结构与算法 · 计算机科学 2022-04-26 Ruixi Luo , Taikun Zhu , Kai Jin

Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$…

数据结构与算法 · 计算机科学 2016-04-08 Paweł Gawrychowski , Tomasz Kociumaka , Wojciech Rytter , Tomasz Waleń

In this paper we define a new problem, motivated by computational biology, $LCSk$ aiming at finding the maximal number of $k$ length $substrings$, matching in both input strings while preserving their order of appearance. The traditional…

数据结构与算法 · 计算机科学 2014-02-11 Gary Benson , Avivit Levy , Riva Shalom

A superpermutation is a sequence that contains every permutation of $n$ distinct symbols as a contiguous substring. For instance, a valid example for three symbols is a sequence that contains all six permutations. This paper introduces a…

离散数学 · 计算机科学 2025-05-19 Dhruv Ajmera

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,…

数据结构与算法 · 计算机科学 2020-03-25 Kiichi Watanabe , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

We consider the $(1+\epsilon)$-approximate nearest neighbor search problem: given a set $X$ of $n$ points in a $d$-dimensional space, build a data structure that, given any query point $y$, finds a point $x \in X$ whose distance to $y$ is…

数据结构与算法 · 计算机科学 2018-07-03 Piotr Indyk , Tal Wagner
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