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Two recent lower bounds on the compressibility of repetitive sequences, $\delta \le \gamma$, have received much attention. It has been shown that a length-$n$ string $S$ over an alphabet of size $\sigma$ can be represented within the…

Data Structures and Algorithms · Computer Science 2023-11-10 Tomasz Kociumaka , Gonzalo Navarro , Francisco Olivares

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…

Data Structures and Algorithms · Computer Science 2025-05-22 Ahsan Sanaullah , Degui Zhi , Shaojie Zhang

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

Practical data structures for the edit-sensitive parsing (ESP) are proposed. Given a string S, its ESP tree is equivalent to a context-free grammar G generating just S, which is represented by a DAG. Using the succinct data structures for…

Data Structures and Algorithms · Computer Science 2015-03-17 Naoya Kishiue , Masaya Nakahara , Shirou Maruyama , Hiroshi Sakamoto

Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the approximate pattern matching problem asks for computation of a particular \emph{distance} function between $P$ and every $m$-substring of $T$. We consider a…

Data Structures and Algorithms · Computer Science 2019-07-24 Jan Studený , Przemysław Uznański

The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…

Data Structures and Algorithms · Computer Science 2025-04-07 Nicola Cotumaccio

Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…

Data Structures and Algorithms · Computer Science 2025-09-22 Hamed Hasibi , Neerja Mhaskar , W. F. Smyth

The constrained LCS problem asks one to find a longest common subsequence of two input strings $A$ and $B$ with some constraints. The STR-IC-LCS problem is a variant of the constrained LCS problem, where the solution must include a given…

Data Structures and Algorithms · Computer Science 2017-03-16 Keita Kuboi , Yuta Fujishige , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

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…

Data Structures and Algorithms · Computer Science 2011-10-21 Francisco Claude , Gonzalo Navarro

Adaptations of features commonly applied in the field of visual computing, co-occurrence matrix (COM) and run-length matrix (RLM), are proposed for the similarity computation of strings in general (words, phrases, codes and texts). The…

Machine Learning · Computer Science 2026-05-15 E. O. Rodrigues , D. Casanova , M. Teixeira , V. Pegorini , F. Favarim , E. Clua , A. Conci , Panos Liatsis

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 this paper we consider the basic variant where the pattern is…

Data Structures and Algorithms · Computer Science 2024-02-15 Philip Bille , Inge Li Gørtz , Teresa Anna Steiner

The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…

Data Structures and Algorithms · Computer Science 2024-03-12 R. Krithika , V. K. Kutty Malu , Prafullkumar Tale

Given a pattern x of length m and a text y of length n, both over an ordered alphabet, the order-preserving pattern matching problem consists in finding all substrings of the text with the same relative order as the pattern. It is an…

Data Structures and Algorithms · Computer Science 2015-01-19 Simone Faro , Oğuzhan Külekci

We show how to compute the edit distance between two strings of length n up to a factor of 2^{\~O(sqrt(log n))} in n^(1+o(1)) time. This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time,…

Data Structures and Algorithms · Computer Science 2011-09-27 Alexandr Andoni , Krzysztof Onak

In this paper we revisit the classical regular expression matching problem, namely, given a regular expression $R$ and a string $Q$, decide if $Q$ matches one of the strings specified by $R$. Let $m$ and $n$ be the length of $R$ and $Q$,…

Data Structures and Algorithms · Computer Science 2007-05-23 Philip Bille

Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient…

Data Structures and Algorithms · Computer Science 2017-03-28 Michał Adamczyk , Mai Alzamel , Panagiotis Charalampopoulos , Costas S. Iliopoulos , Jakub Radoszewski

In many applications, it is necessary to determine the string similarity. Edit distance[WF74] approach is a classic method to determine Field Similarity. A well known dynamic programming algorithm [GUS97] is used to calculate edit distance…

Data Structures and Algorithms · Computer Science 2007-05-23 Qi Xiao Yang , Sung Sam Yuan , Lu Chun , Li Zhao , Sun Peng

We describe how, given a text $T [1..n]$ and a positive constant $\epsilon$, we can build a simple $O (z \log n)$-space index, where $z$ is the number of phrases in the LZ77 parse of $T$, such that later, given a pattern $P [1..m]$, in $O…

Data Structures and Algorithms · Computer Science 2022-12-06 Nick Fagan , Jorge Hermo González , Travis Gagie

We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result we combine several recent findings,…

Data Structures and Algorithms · Computer Science 2019-09-06 Anders Roy Christiansen , Mikko Berggren Ettienne , Tomasz Kociumaka , Gonzalo Navarro , Nicola Prezza

We present an algorithm that, given an index $t$, produces the $t$-th (lexicographically ordered) answer of an MSO query over a string. The algorithm requires linear-time preprocessing, and builds a data structure that answers each of these…

Data Structures and Algorithms · Computer Science 2026-03-16 Martín Muñoz