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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

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

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

We propose a simple linear-time on-line algorithm for constructing a position heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it…

数据结构与算法 · 计算机科学 2015-03-19 Gregory Kucherov

Let $\Sigma$ and $\Pi$ be disjoint alphabets, respectively called the static alphabet and the parameterized alphabet. Two strings $x$ and $y$ over $\Sigma \cup \Pi$ of equal length are said to parameterized match (p-match) if there exists a…

数据结构与算法 · 计算机科学 2021-02-05 Noriki Fujisato , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a string $T$ of length $n$ has $O(n)$ nodes and edges, and the string label of each edge is encoded by a pair of positions in $T$.…

数据结构与算法 · 计算机科学 2019-04-11 Diptarama Hendrian , Takuya Takagi , Shunsuke Inenaga

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…

The suffix trees are fundamental data structures for various kinds of string processing. The suffix tree of a text string $T$ of length $n$ has $O(n)$ nodes and edges, and the string label of each edge is encoded by a pair of positions in…

数据结构与算法 · 计算机科学 2023-12-06 Diptarama Hendrian , Takuya Takagi , Shunsuke Inenaga , Keisuke Goto , Mitsuru Funakoshi

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

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

Position heaps are index structures of text strings used for the string matching problem. They are rooted trees whose edges and nodes are labeled and numbered, respectively. This paper is concerned with variants of the inverse problem of…

数据结构与算法 · 计算机科学 2022-12-13 Koshiro Kumagai , Diptarama Hendrian , Ryo Yoshinaka , Ayumi Shinohara

Parameterized strings are a generalization of strings in that their characters are drawn from two different alphabets, where one is considered to be the alphabet of static characters and the other to be the alphabet of parameter characters.…

数据结构与算法 · 计算机科学 2022-09-01 Daiki Hashimoto , Diptarama Hendrian , Dominik Köppl , Ryo Yoshinaka , Ayumi Shinohara

In this paper, we describe a new type of match between a pattern and a text that aren't necessarily maximal in the query, but still contain useful matching information: locally maximal exact matches (LEMs). There are usually a large amount…

数据结构与算法 · 计算机科学 2025-05-22 Ahsan Sanaullah , Degui Zhi , Shaojie Zhang

The Cartesian-tree pattern matching is a recently introduced scheme of pattern matching that detects fragments in a sequential data stream which have a similar structure as a query pattern. Formally, Cartesian-tree pattern matching seeks…

数据结构与算法 · 计算机科学 2021-08-17 Akio Nishimoto , Noriki Fujisato , Yuto Nakashima , Shunsuke Inenaga

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

数据结构与算法 · 计算机科学 2022-07-01 Anas Al-okaily , Abdelghani Tbakhi

We deal with the problem of maintaining the suffix tree indexing structure for a fully-online collection of multiple strings, where a new character can be prepended to any string in the collection at any time. The only previously known…

数据结构与算法 · 计算机科学 2020-05-05 Shunsuke Inenaga

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and…

数据结构与算法 · 计算机科学 2013-01-15 Travis Gagie , Wing-Kai Hon , Tsung-Han Ku

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

Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We…

数据结构与算法 · 计算机科学 2020-11-17 Panagiotis Charalampopoulos , Tomasz Kociumaka , Philip Wellnitz

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
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