Related papers: Space Lower Bounds for Online Pattern Matching
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give…
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…
Text-to-pattern distance is a fundamental problem in string matching, where given a pattern of length $m$ and a text of length $n$, over an integer alphabet, we are asked to compute the distance between pattern and the text at every…
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…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
The problem of finding \emph{distance} between \emph{pattern} of length $m$ and \emph{text} of length $n$ is a typical way of generalizing pattern matching to incorporate dissimilarity score. For both Hamming and $L_1$ distances only a…
We give cell-probe bounds for the computation of edit distance, Hamming distance, convolution and longest common subsequence in a stream. In this model, a fixed string of $n$ symbols is given and one $\delta$-bit symbol arrives at a time in…
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…
For online matching with the line metric, we present a lower bound of $\Omega(\log n)$ on the approximation ratio of any online (possibly randomized) algorithm. This beats the previous best lower bound of $\Omega(\sqrt{\log n})$ and matches…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive…
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…
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 $T$…
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 decades-old Pattern Matching with Edits problem, given a length-$n$ string $T$ (the text), a length-$m$ string $P$ (the pattern), and a positive integer $k$ (the threshold), asks to list all fragments of $T$ that are at edit distance at…
We investigate the randomized and quantum communication complexity of the Hamming Distance problem, which is to determine if the Hamming distance between two n-bit strings is no less than a threshold d. We prove a quantum lower bound of…
The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence…
We show tight bounds for online Hamming distance computation in the cell-probe model with word size w. The task is to output the Hamming distance between a fixed string of length n and the last n symbols of a stream. We give a lower bound…
We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…