Related papers: Efficiently Finding All Minimal and Shortest Absen…
Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…
A minimal absent word of a sequence x, is a sequence yt hat is not a factorof x, but all of its proper factors are factors of x as well. The set of minimal absent words uniquely defines the sequence itself. In recent times minimal absent…
Longest Increasing Subsequence (LIS) is a fundamental statistic of a sequence, and has been studied for decades. While the LIS of a sequence of length $n$ can be computed exactly in time $O(n\log n)$, the complexity of estimating the…
A substring $u$ of a string $T$ is called a minimal unique substring (MUS) of $T$ if $u$ occurs exactly once in $T$ and any proper substring of $u$ occurs at least twice in $T$. A string $w$ is called a minimal absent word (MAW) of $T$ if…
We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…
We study the following substring suffix selection problem: given a substring of a string T of length n, compute its k-th lexicographically smallest suffix. This a natural generalization of the well-known question of computing the maximal…
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…
In this report, we consider Adelman's algorithm for generating shortest permutation strings. We introduce a new representation approach which reveals some properties of Adelman's algorithm.
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i.e., random subsequences of the…
This paper considers the problem of maintaining statistic aggregates over the last W elements of a data stream. First, the problem of counting the number of 1's in the last W bits of a binary stream is considered. A lower bound of…
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation,…
It is shown that the N-extended super $w_n$\ string can be obtained as a special class of vacua of both the N-extended super $w_{n+1}$\ string and the (N+1)-extended super $w_n$\ string. This hierarchy of super $w$\ string theories includes…
The longest common subsequence (LCS) is a fundamental problem in string processing which has numerous algorithmic studies, extensions, and applications. A sequence $u_1, \ldots, u_f$ of $f$ strings s said to be an ($f$-)segmentation of a…
A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…
We present an online algorithm to deal with pattern matching in strings. The problem we investigate is commonly known as string matching with mismatches in which the objective is to report the number of characters that match when a pattern…
Let $S$ be a string of length $n$. In this paper we introduce the notion of \emph{string attractor}: a subset of the string's positions $[1,n]$ such that every distinct substring of $S$ has an occurrence crossing one of the attractor's…
The expected length of longest common subsequences is a problem that has been in the literature for at least twenty five years. Determining the limiting constants \gamma_k appears to be quite difficult, and the current best bounds leave…
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 consider the information extraction framework known as document spanners, and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential…