Related papers: Faster Approximate Pattern Matching: A Unified App…
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…
Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Given a positive distance function…
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…
The NP-complete Permutation Pattern Matching problem asks whether a permutation P (the pattern) can be matched into a permutation T (the text). A matching is an order-preserving embedding of P into T. In the Generalized Permutation Pattern…
We present an algorithm for approximating the edit distance between two strings of length $n$ in time $n^{1+\varepsilon}$ up to a constant factor, for any $\varepsilon>0$. Our result completes a research direction set forth in the recent…
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…
In the longest common substring problem, we are given two strings of length $n$ and must find a substring of maximal length that occurs in both strings. It is well known that the problem can be solved in linear time, but the solution is not…
The classic string indexing problem is to preprocess a string $S$ into a compact data structure that supports efficient subsequent pattern matching queries, that is, given a pattern string $P$, report all occurrences of $P$ within $S$. In…
The edit distance between two strings is defined as the smallest number of insertions, deletions, and substitutions that need to be made to transform one of the strings to another one. Approximating edit distance in subquadratic time is…
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…
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…
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently,…
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…
We revisit the exact shortest unique substring (SUS) finding problem, and propose its approximate version where mismatches are allowed, due to its applications in subfields such as computational biology. We design a generic in-place…
A similarity join aims to find all similar pairs between two collections of records. Established approaches usually deal with synthetic differences like typos and abbreviations, but neglect the semantic relations between words. Such…
In runtime verification, pattern matching, which searches for occurrences of a specific pattern within a word, provides more information than a simple violation detection of the monitored property, by locating concrete evidence of the…
The Dyck language, which consists of well-balanced sequences of parentheses, is one of the most fundamental context-free languages. The Dyck edit distance quantifies the number of edits (character insertions, deletions, and substitutions)…
Edit distance is an important measure of string similarity. It counts the number of insertions, deletions and substitutions one has to make to a string $x$ to get a string $y$. In this paper we design an almost linear-size sketching scheme…
Ochem, Rampersad, and Shallit gave various examples of infinite words avoiding what they called approximate repetitions. An approximate repetition is a factor of the form xx', where x and x' are close to being identical. In their work, they…
We study the problem of approximating edit distance in sublinear time. This is formalized as the $(k,k^c)$-Gap Edit Distance problem, where the input is a pair of strings $X,Y$ and parameters $k,c>1$, and the goal is to return YES if…