Related papers: A Simple Reduction for Full-Permuted Pattern Match…
Detecting all the strings that occur in a text more frequently or less frequently than expected according to an IID or a Markov model is a basic problem in string mining, yet current algorithms are based on data structures that are either…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
This study develops an algorithm to solve a variation of the Shortest Common Superstring (SCS) problem. There are two modifications to the base SCS problem. First, one string in the set S is allowed to have up to K mistakes, defined as not…
Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…
A superpermutation is a sequence that contains every permutation of $n$ distinct symbols as a contiguous substring. For instance, a valid example for three symbols is a sequence that contains all six permutations. This paper introduces a…
We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous…
We define the ``shift-match number'' for a binary string and we compute the probability of occurrence of a given string as a subsequence in longer strings in terms of its shift-match number. We thus prove that the string matching…
We present a polynomial-time algorithm that discovers all maximal patterns in a point set, $D\subset\mathbb{R}^k$, that are related by transformations in a user-specified class, $F$, of bijections over $\mathbb{R}^k$. We also present a…
We introduce the following natural generalization of trace reconstruction, parameterized by a deletion probability $\delta \in (0,1)$ and length $n$: There is a length $n$ string of probabilities, $S=p_1,\ldots,p_n,$ and each "trace" is…
Bitstrings can be permuted via permutations and compared via the lexicographic order. In this paper we study the complexity of finding a minimum of a bitstring via given permutations. As a global optima is known to be NP-complete, we study…
In the trace reconstruction problem our goal is to learn an unknown string $x\in \{0,1\}^n$ given independent traces of $x$. A trace is obtained by independently deleting each bit of $x$ with some probability $\delta$ and concatenating the…
Let $\Sigma$ be an alphabet. For two strings $X$, $Y$, and a constrained string $P$ over the alphabet $\Sigma$, the constrained longest common subsequence and substring problem for two strings $X$ and $Y$ with respect to $P$ is to find a…
We introduce a novel definition of approximate palindromes in strings, and provide an algorithm to find all maximal approximate palindromes in a string with up to $k$ errors. Our definition is based on the usual edit operations of…
In this article, we study the problem of finding the longest common separable pattern between several permutations. We give a polynomial-time algorithm when the number of input permutations is fixed and show that the problem is NP-hard for…
The NP-complete Permutation Pattern Matching problem asks whether a $k$-permutation $P$ is contained in a $n$-permutation $T$ as a pattern. This is the case if there exists an order-preserving embedding of $P$ into $T$. In this paper, we…
We study the query complexity of exactly reconstructing a string from adaptive queries, such as substring, subsequence, and jumbled-index queries. Such problems have applications, e.g., in computational biology. We provide a number of new…
Given a string $P$ of length $m$, a longer string $T$ of length $n>m$, and two integers $l\geq 0$ and $r\geq 0$, the context of $P$ in $T$ is the set of all string pairs $(L,R)$, with $|L|=l$ and $|R|=r$, such that the string $LPR$ occurs…
In the standard trace reconstruction problem, the goal is to \emph{exactly} reconstruct an unknown source string $\mathsf{x} \in \{0,1\}^n$ from independent "traces", which are copies of $\mathsf{x}$ that have been corrupted by a…
This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model. More concretely, the goal of the problem is to identify an unknown string $S$…
The abelian pattern matching problem consists in finding all substrings of a text which are permutations of a given pattern. This problem finds application in many areas and can be solved in linear time by a naive sliding window approach.…