Related papers: Hidden Words Statistics for Large Patterns
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…
Detecting and counting copies of permutation patterns are fundamental algorithmic problems, with applications in the analysis of rankings, nonparametric statistics, and property testing tasks such as independence and quasirandomness…
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…
Motivated by the recent proof of the Stanley-Wilf conjecture, we study the asymptotic behavior of the number of permutations avoiding a generalized pattern. Generalized patterns allow the requirement that some pairs of letters must be…
The $k$-mismatch problem consists in computing the Hamming distance between a pattern $P$ of length $m$ and every length-$m$ substring of a text $T$ of length $n$, if this distance is no more than $k$. In many real-world applications, any…
Word matches are often used in sequence comparison methods, either as a measure of sequence similarity or in the first search steps of algorithms such as BLAST or BLAT. The D2 statistic is the number of matches of words of k letters between…
We study the classic Text-to-Pattern Hamming Distances problem: given a pattern $P$ of length $m$ and a text $T$ of length $n$, both over a polynomial-size alphabet, compute the Hamming distance between $P$ and $T[i\, .\, . \, i+m-1]$ for…
Permutation $\sigma$ appears in permutation $\pi$ if there exists a subsequence of $\pi$ that is order-isomorphic to $\sigma$. The natural question is to check if $\sigma$ appears in $\pi$, and if so count the number of occurrences. We know…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
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…
A string $w$ is called a minimal absent word (MAW) for another string $T$ if $w$ does not occur (as a substring) in $T$ and any proper substring of $w$ occurs in $T$. State-of-the-art data structures for reporting the set $\mathsf{MAW}(T)$…
Regular expressions constitute a fundamental notion in formal language theory and are frequently used in computer science to define search patterns. A classic algorithm for these problems constructs and simulates a non-deterministic finite…
In this paper we consider several variants of the pattern matching problem. In particular, we investigate the following problems: 1) Pattern matching with k mismatches; 2) Approximate counting of mismatches; and 3) Pattern matching with…
We consider the approximate pattern matching problem under edit distance. In this problem we are given a pattern $P$ of length $w$ and a text $T$ of length $n$ over some alphabet $\Sigma$, and a positive integer $k$. The goal is to find all…
We introduce a permutation analogue of the celebrated Szemeredi Regularity Lemma, and derive a number of consequences. This tool allows us to provide a structural description of permutations which avoid a specified pattern, a result that…
In this paper, we explore worst-case solutions for the problems of single and multiple matching on strings in the word RAM model with word length w. In the first problem, we have to build a data structure based on a pattern p of length m…
We study the "set parameterized matching" problem, a generalization of the classical parameterized matching problem introduced by Baker. In set parameterized matching, both the pattern and text are sequences where each position contains a…
Countless variants of the Lempel-Ziv compression are widely used in many real-life applications. This paper is concerned with a natural modification of the classical pattern matching problem inspired by the popularity of such compression…
Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation…
Sparse representation has been applied successfully in abnormal event detection, in which the baseline is to learn a dictionary accompanied by sparse codes. While much emphasis is put on discriminative dictionary construction, there are no…