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We consider several types of internal queries: questions about subwords of a text. As the main tool we develop an optimal data structure for the problem called here internal pattern matching. This data structure provides constant-time answers to queries about occurrences of one subword $x$ in another subword $y$ of a given text, assuming that $|y|=mathcal{O}(|x|)$, which allows for a constant-space representation of all occurrences. This problem can be viewed as a natural extension of the well-studied pattern matching problem. The data structure has linear size and admits a linear-time construction algorithm. Using the solution to the internal pattern matching problem, we obtain very efficient data structures answering queries about: primitivity of subwords, periods of subwords, general substring compression, and cyclic equivalence of two subwords. All these results improve upon the best previously known counterparts. The linear construction time of our data structure also allows to improve the algorithm for finding $delta$-subrepetitions in a text (a more general version of maximal repetitions, also called runs). For any fixed $delta$ we obtain the first linear-time algorithm, which matches the linear time complexity of the algorithm computing runs. Our data structure has already been used as a part of the efficient solutions for subword suffix rank & selection, as well as substring compression using Burrows-Wheeler transform composed with run-length encoding.
We investigate the problem of deterministic pattern matching in multiple streams. In this model, one symbol arrives at a time and is associated with one of s streaming texts. The task at each time step is to report if there is a new match between a f
Given a string $T$ of length $n$ over an alphabet $Sigmasubset {1,2,ldots,n^{O(1)}}$ of size $sigma$, we are to preprocess $T$ so that given a range $[i,j]$, we can return a representation of a shortest string over $Sigma$ that is absent in the fragm
We consider a class of pattern matching problems where a normalising transformation is applied at every alignment. Normalised pattern matching plays a key role in fields as diverse as image processing and musical information processing where applicat
We consider the following stochastic matching problem on both weighted and unweighted graphs: A graph $G(V, E)$ along with a parameter $p in (0, 1)$ is given in the input. Each edge of $G$ is realized independently with probability $p$. The goal is t
In this work, we study longest common substring, pattern matching, and wildcard pattern matching in the asymmetric streaming model. In this streaming model, we have random access to one string and streaming access to the other one. We present streami