相关论文: New Algorithms for Regular Expression Matching

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…

It is well known that n integers in the range [1,n^c] can be sorted in O(n) time in the RAM model using radix sorting. More generally, integers in any range [1,U] can be sorted in O(n sqrt{loglog n}) time. However, these algorithms use O(n)…

In this paper we describe compressed indexes that support pattern matching queries for strings with wildcards. For a constant size alphabet our data structure uses $O(n\log^{\varepsilon}n)$ bits for any $\varepsilon>0$ and reports all…

In the $k$-mismatch problem, given a pattern and a text of length $n$ and $m$ respectively, we have to find if the text has a sub-string with a Hamming distance of at most $k$ from the pattern. This has been studied in the classical setting…

In the problem of $\texttt{Generalised Pattern Matching}\ (\texttt{GPM})$ [STOC'94, Muthukrishnan and Palem], we are given a text $T$ of length $n$ over an alphabet $\Sigma_T$, a pattern $P$ of length $m$ over an alphabet $\Sigma_P$, and a…

Consider the problem of maintaining a family $F$ of dynamic sets subject to insertions, deletions, and set-intersection reporting queries: given $S,S'\in F$, report every member of $S\cap S'$ in any order. We show that in the word RAM…

Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…

We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…

Regular expression matching is essential for many applications, such as finding patterns in text, exploring substrings in large DNA sequences, or lexical analysis. However, sequential regular expression matching may be time-prohibitive for…

We solve the problems of detecting and counting various forms of regularities in a string represented as a Straight Line Program (SLP). Given an SLP of size $n$ that represents a string $s$ of length $N$, our algorithm compute all runs and…

Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. In the last two…

We revisit the complexity of building, given a two-dimensional string of size $n$, an indexing structure that allows locating all $k$ occurrences of a two-dimensional pattern of size $m$. While a structure of size $\mathcal{O}(n)$ with…

We generalise a multiple string pattern matching algorithm, recently proposed by Fredriksson and Grabowski [J. Discr. Alg. 7, 2009], to deal with arbitrary dictionaries on an alphabet of size $s$. If $r_m$ is the number of words of length…

The longest square subsequence (LSS) problem consists of computing a longest subsequence of a given string $S$ that is a square, i.e., a longest subsequence of form $XX$ appearing in $S$. It is known that an LSS of a string $S$ of length…

The $k$-mappability problem has two integers parameters $m$ and $k$. For every subword of size $m$ in a text $S$, we wish to report the number of indices in $S$ in which the word occurs with at most $k$ mismatches. The problem was lately…

We show that rational data of bounded input length are uniformly distributed with respect to condition numbers of numerical analysis. We deal both with condition numbers of Linear Algebra and with condition numbers for systems of…

Given a text and a pattern over an alphabet, the pattern matching problem searches for all occurrences of the pattern in the text. An equivalence relation $\approx$ is called a substring consistent equivalence relation (SCER), if for two…

We study algorithms for solving the problem of constructing a text (long string) from a dictionary (sequence of small strings). The problem has an application in bioinformatics and has a connection with the Sequence assembly method for…

The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…

Repeat finding in strings has important applications in subfields such as computational biology. The challenge of finding the longest repeats covering particular string positions was recently proposed and solved by \.{I}leri et al., using a…