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Let $\Sigma$ and $\Pi$ be disjoint alphabets of respective size $\sigma$ and $\pi$. Two strings over $\Sigma \cup \Pi$ of equal length are said to parameterized match (p-match) if there is a bijection $f:\Sigma \cup \Pi \rightarrow \Sigma…

数据结构与算法 · 计算机科学 2019-03-18 Noriki Fujisato , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

A parameterized string (p-string) is a string over an alphabet $(\Sigma_{s} \cup \Sigma_{p})$, where $\Sigma_{s}$ and $\Sigma_{p}$ are disjoint alphabets for static symbols (s-symbols) and for parameter symbols (p-symbols), respectively.…

数据结构与算法 · 计算机科学 2023-08-14 Kento Iseri , Tomohiro I , Diptarama Hendrian , Dominik Köppl , Ryo Yoshinaka , Ayumi Shinohara

Two strings $x$ and $y$ over $\Sigma \cup \Pi$ of equal length are said to \emph{parameterized match} (\emph{p-match}) if there is a renaming bijection $f:\Sigma \cup \Pi \rightarrow \Sigma \cup \Pi$ that is identity on $\Sigma$ and…

We consider the $Parameterized$ $Pattern$ $Matching$ problem, where a pattern $P$ matches some location in a text $\mathsf{T}$ iff there is a one-to-one correspondence between the alphabet symbols of the pattern to those of the text. More…

数据结构与算法 · 计算机科学 2016-04-07 Arnab Ganguly , Rahul Shah , Sharma V. Thankachan

The parameterized matching problem is a variant of string matching, which is to search for all parameterized occurrences of a pattern $P$ in a text $T$. In considering matching algorithms, the combinatorial natures of strings, especially…

数据结构与算法 · 计算机科学 2023-06-21 Haruki Ideguchi , Diptarama Hendrian , Ryo Yoshinaka , Ayumi Shinohara

In this paper, we propose a new indexing structure for parameterized strings which we call PLSTs, by generalizing linear-size suffix tries for ordinary strings. Two parameterized strings are said to match if there is a bijection on the…

数据结构与算法 · 计算机科学 2019-09-05 Katsuhito Nakashima , Diptarama Hendrian , Ryo Yoshinaka , Ayumi Shinohara

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

Suffix trees and suffix arrays are two of the most widely used data structures for text indexing. Each uses linear space and can be constructed in linear time for polynomially sized alphabets. However, when it comes to answering queries…

数据结构与算法 · 计算机科学 2013-11-08 Richard Cole , Tsvi Kopelowitz , Moshe Lewenstein

Two strings of equal length are said to parameterized match if there is a bijection that maps the characters of one string to those of the other string, so that two strings become identical. The parameterized pattern matching problem is,…

数据结构与算法 · 计算机科学 2018-08-06 Noriki Fujisato , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

Given two strings $T$ and $S$ and a set of strings $P$, for each string $p \in P$, consider the unique substrings of $T$ that have $p$ as their prefix and $S$ as their suffix. Two problems then come to mind; the first problem being the…

数据结构与算法 · 计算机科学 2022-04-19 Laurentius Leonard , Ken Tanaka

In this work, we tackle a natural variation of the String Matching Problem on the case of a dynamic pattern, that is, given a static text $T$ and a pattern $P$, we want to support character additions and deletions to the pattern, and after…

数据结构与算法 · 计算机科学 2025-06-16 Bruno Monteiro , Vinicius dos Santos

We propose a new indexing structure for parameterized strings, called parameterized position heap. Parameterized position heap is applicable for parameterized pattern matching problem, where the pattern matches a substring of the text if…

数据结构与算法 · 计算机科学 2017-04-19 Diptarama , Takashi Katsura , Yuhei Otomo , Kazuyuki Narisawa , Ayumi Shinohara

We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

数据结构与算法 · 计算机科学 2011-10-14 Philip Bille , Inge Li Goertz , Hjalte Wedel Vildhøj , David Kofoed Wind

We present the first worst-case linear time algorithm that directly computes the parameterized suffix and LCP arrays for constant sized alphabets. Previous algorithms either required quadratic time or the parameterized suffix tree to be…

数据结构与算法 · 计算机科学 2019-06-04 Noriki Fujisato , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

The classic string indexing problem is to preprocess a string S into a compact data structure that supports efficient pattern matching queries. Typical queries include existential queries (decide if the pattern occurs in S), reporting…

数据结构与算法 · 计算机科学 2021-02-05 Philip Bille , Inge Li Gørtz , Max Rishøj Pedersen , Teresa Anna Steiner

We present parallel algorithms for exact and approximate pattern matching with suffix arrays, using a CREW-PRAM with $p$ processors. Given a static text of length $n$, we first show how to compute the suffix array interval of a given…

数据结构与算法 · 计算机科学 2016-06-09 Johannes Fischer , Dominik Köppl , Florian Kurpicz

We study the fundamental question of how efficiently suffix array entries can be accessed when the array cannot be stored explicitly. The suffix array $SA_T[1..n]$ of a text $T$ of length $n$ encodes the lexicographic order of its suffixes…

数据结构与算法 · 计算机科学 2025-10-23 Dominik Kempa , Tomasz Kociumaka

In this paper we describe a data structure that supports pattern matching queries on a dynamically arriving text over an alphabet ofconstant size. Each new symbol can be prepended to $T$ in O(1) worst-case time. At any moment, we can report…

数据结构与算法 · 计算机科学 2013-07-09 Gregory Kucherov , Yakov Nekrich

The palindrome pattern matching (pal-matching) is a kind of generalized pattern matching, in which two strings $x$ and $y$ of same length are considered to match (pal-match) if they have the same palindromic structures, i.e., for any…

数据结构与算法 · 计算机科学 2023-04-17 Shinya Nagashita , Tomohiro I

Given a pattern string $P$ of length $n$ consisting of $\delta$ distinct characters and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet $\Sigma$ of size $\Delta$, the {\em exact string…

数据结构与算法 · 计算机科学 2015-12-14 Srikrishnan Divakaran
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