Related papers: Algorithms for Jumbled Pattern Matching in Strings
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 $d$-dimensional pattern matching problem is to find an occurrence of a pattern of length $m \times \dots \times m$ within a text of length $n \times \dots \times n$, with $n \ge m$. This task models various problems in text and image…
Motif searching is an important step in the detection of rare events occurring in a set of DNA or protein sequences. One formulation of the problem is known as (l,d)-motif search or Planted Motif Search (PMS). In PMS we are given two…
String matching is one of the most fundamental problems in computer science. A natural problem is to determine the number of characters that need to be queried (i.e. the decision tree complexity) in a string in order to decide whether this…
The online square detection problem is to detect the first occurrence of a square in a string whose characters are provided as input one at a time. Recall that a square is a string that is a concatenation of two identical strings. In this…
A weighted string, also known as a position weight matrix, is a sequence of probability distributions over some alphabet. We revisit the Weighted Shortest Common Supersequence (WSCS) problem, introduced by Amir et al. [SPIRE 2011], that is,…
In this paper, we consider the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). The problem is as follows. For a positive integer $n$, a sequence of n strings $S=(s^1,\dots,s^n)$ is given. We should…
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
Detection of symmetry is vital to problem solving. Most of the problems of computer vision and computer graphics and machine intelligence in general, can be reduced to symmetry detection problem. Unstructured search problem can also be…
The domains of data mining and knowledge discovery make use of large amounts of textual data, which need to be handled efficiently. Specific problems, like finding the maximum weight ordered common subset of a set of ordered sets or…
Parikh automata extend automata with counters whose values can only be tested at the end of the computation, with respect to membership into a semi-linear set. Parikh automata have found several applications, for instance in transducer…
We say a string has a cadence if a certain character is repeated at regular intervals, possibly with intervening occurrences of that character. We call the cadence anchored if the first interval must be the same length as the others. We…
Pattern matching with wildcards is the problem of finding all factors of a text $t$ of length $n$ that match a pattern $x$ of length $m$, where wildcards (characters that match everything) may be present. In this paper we present a number…
Pattern matching queries on strings can be solved in linear time by Knuth-Morris-Pratt (KMP) algorithm. In 1973, Weiner introduced the suffix tree of a string [FOCS 1973] and showed that the seemingly more difficult problem of computing…
For a string $S$, a palindromic substring $S[i..j]$ is said to be a \emph{shortest unique palindromic substring} ($\mathit{SUPS}$) for an interval $[s, t]$ in $S$, if $S[i..j]$ occurs exactly once in $S$, the interval $[i, j]$ contains $[s,…
In the Pattern Masking for Dictionary Matching (PMDM) problem, we are given a dictionary $\mathcal{D}$ of $d$ strings, each of length $\ell$, a query string $q$ of length $\ell$, and a positive integer $z$, and we are asked to compute a…
Word2vec (Mikolov et al., 2013) has proven to be successful in natural language processing by capturing the semantic relationships between different words. Built on top of single-word embeddings, paragraph vectors (Le and Mikolov, 2014)…
Given a string $s$ of length $n$ over a general alphabet and an integer $k$, the problem is to decide whether $s$ is a concatenation of $k$ nonempty palindromes. Two previously known solutions for this problem work in time $O(kn)$ and…
Let us consider the Multiple String Matching Problem. In this problem, we consider a long string, denoted by $t$, of length $n$. This string is referred to as a text. We also consider a sequence of $m$ strings, denoted by $S$, which we…
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…