Related papers: On the Average-case Complexity of Pattern Matching…
Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the…
Fast matching of regular expressions with bounded repetition, aka counting, such as (ab){50,100}, i.e., matching linear in the length of the text and independent of the repetition bounds, has been an open problem for at least two decades.…
The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…
We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have…
In a simple pattern matching problem one has a pattern $w$ and a text $t$, which are words over a finite alphabet $\Sigma$. One may ask whether $w$ occurs in $t$, and if so, where? More generally, we may have a set $P$ of patterns and a set…
Zimin words are very special finite words which are closely related to the pattern-avoidability problem. This problem consists in testing if an instance of a given pattern with variables occurs in almost all words over any finite alphabet.…
Considering matrices with missing entries, we study NP-hard matrix completion problems where the resulting completed matrix shall have limited (local) radius. In the pure radius version, this means that the goal is to fill in the entries…
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…
This paper addresses the online exact string matching problem which consists in finding all occurrences of a given pattern p in a text t. It is an extensively studied problem in computer science, mainly due to its direct applications to…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
Patterns provide a concise, syntactic way of describing a set of strings, but their expressive power comes at a price: a number of fundamental decision problems concerning (erasing) pattern languages, such as the membership problem and…
In this paper, we revisit the much studied problem of Pattern Matching with Swaps (Swap Matching problem, for short). We first present a graph-theoretic model, which opens a new and so far unexplored avenue to solve the problem. Then, using…
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. Sampled string…
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…
We study pattern matching problems on two major representations of uncertain sequences used in molecular biology: weighted sequences (also known as position weight matrices, PWM) and profiles (i.e., scoring matrices). In the simple version,…
A family of comparison-based exact pattern matching algorithms is described. They utilize multi-dimensional arrays in order to process more than one adjacent text window in each iteration of the search cycle. This approach leads to a lower…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for…
Error Tree is a novel tree structure that is mainly oriented to solve the approximate pattern matching problems, Hamming and edit distances, as well as the wildcards matching problem. The input is a text of length $n$ over a fixed alphabet…
As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…
Term pattern matching is the problem of finding all pattern matches in a subject term, given a set of patterns. Finding efficient algorithms for this problem is an important direction for research [19]. We present a new set automaton…