Related papers: The k-mismatch problem revisited

We consider the streaming complexity of a fundamental task in approximate pattern matching: the $k$-mismatch problem. It asks to compute Hamming distances between a pattern of length $n$ and all length-$n$ substrings of a text for which the…

In the $k$-mismatch problem we are given a pattern of length $n$ and a text and must find all locations where the Hamming distance between the pattern and the text is at most $k$. A series of recent breakthroughs have resulted in an…

We present a new streaming algorithm for the $k$-Mismatch problem, one of the most basic problems in pattern matching. Given a pattern and a text, the task is to find all substrings of the text that are at the Hamming distance at most $k$…

The text-to-pattern Hamming distances problem asks to compute the Hamming distances between a given pattern of length $m$ and all length-$m$ substrings of a given text of length $n\ge m$. We focus on the $k$-mismatch version of the problem,…

We revisit the $k$-mismatch problem in the streaming model on a pattern of length $m$ and a streaming text of length $n$, both over a size-$\sigma$ alphabet. The current state-of-the-art algorithm for the streaming $k$-mismatch problem, by…

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…

In this work, we revisit the fundamental and well-studied problem of approximate pattern matching under edit distance. Given an integer $k$, a pattern $P$ of length $m$, and a text $T$ of length $n \ge m$, the task is to find substrings of…

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…

Given a pattern of length $m$ and a text of length $n$, the goal in $k$-mismatch pattern matching is to compute, for every $m$-substring of the text, the exact Hamming distance to the pattern or report that it exceeds $k$. This can be…

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…

The longest common substring with $k$-mismatches problem is to find, given two strings $S_1$ and $S_2$, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ and $A_2$ is $\le k$. We introduce a…

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…

The recently introduced longest common substring with $k$-mismatches ($k$-LCF) problem is to find, given two sequences $S_1$ and $S_2$ of length $n$ each, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance…

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…

We consider the problem of computing distance between a pattern of length $n$ and all $n$-length subwords of a text in the streaming model. In the streaming setting, only the Hamming distance ($L_0$) has been studied. It is known that…

In this paper we give an algorithm for streaming $k$-edit approximate pattern matching which uses space $\widetilde{O}(k^2)$ and time $\widetilde{O}(k^2)$ per arriving symbol. This improves substantially on the recent algorithm of…

We consider the problem of computing a $(1+\epsilon)$-approximation of the Hamming distance between a pattern of length $n$ and successive substrings of a stream. We first look at the one-way randomised communication complexity of this…

We design and implement two single-pass semi-streaming algorithms for the maximum weight $k$-disjoint matching ($k$-DM) problem. Given an integer $k$, the $k$-DM problem is to find $k$ pairwise edge-disjoint matchings such that the sum of…

In this work, we address the problem of approximate pattern matching with wildcards. Given a pattern $P$ of length $m$ containing $D$ wildcards, a text $T$ of length $n$, and an integer $k$, our objective is to identify all fragments of $T$…

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…