Related papers: On Estimating Edit Distance: Alignment, Dimension …

We consider the problem of preprocessing two strings $S$ and $T$, of lengths $m$ and $n$, respectively, in order to be able to efficiently answer the following queries: Given positions $i,j$ in $S$ and positions $a,b$ in $T$, return the…

We consider the approximate pattern matching problem under edit distance. In this problem we are given a pattern $P$ of length $w$ and a text $T$ of length $n$ over some alphabet $\Sigma$, and a positive integer $k$. The goal is to find all…

We study the classical approximate string matching problem, that is, given strings $P$ and $Q$ and an error threshold $k$, find all ending positions of substrings of $Q$ whose edit distance to $P$ is at most $k$. Let $P$ and $Q$ have…

A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…

In this paper we provide a new locally consistent decomposition of strings. Each string $x$ is decomposed into blocks that can be described by grammars of size $\widetilde{O}(k)$ (using some amount of randomness). If we take two strings $x$…

Fitting distances to tree metrics and ultrametrics are two widely used methods in hierarchical clustering, primarily explored within the context of numerical taxonomy. Given a positive distance function…

An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…

The approximate string matching is a fundamental and recurrent problem that arises in most computer science fields. This problem can be defined as follows: Let $D=\{x_1,x_2,\ldots x_d\}$ be a set of $d$ words defined on an alphabet…

We show that in the document exchange problem, where Alice holds $x \in \{0,1\}^n$ and Bob holds $y \in \{0,1\}^n$, Alice can send Bob a message of size $O(K(\log^2 K+\log n))$ bits such that Bob can recover $x$ using the message and his…

Dynamic Time Warping (DTW) is a widely used similarity measure for comparing strings that encode time series data, with applications to areas including bioinformatics, signature verification, and speech recognition. The standard…

We introduce the notion of Levenshtein graphs, an analog to Hamming graphs but using the edit distance instead of the Hamming distance; in particular, Levenshtein graphs allow for underlying strings (nodes) of different lengths. We…

In Pattern Matching with Weighted Edits (PMWED), we are given a pattern $P$ of length $m$, a text $T$ of length $n$, a positive threshold $k$, and oracle access to a weight function that specifies the costs of edits (depending on the…

The graph edit distance is an intuitive measure to quantify the dissimilarity of graphs, but its computation is NP-hard and challenging in practice. We introduce methods for answering nearest neighbor and range queries regarding this…

As text-based speech editing becomes increasingly prevalent, the demand for unrestricted free-text editing continues to grow. However, existing speech editing techniques encounter significant challenges, particularly in maintaining…

This paper proposes a novel acoustic word embedding called Acoustic Neighbor Embeddings where speech or text of arbitrary length are mapped to a vector space of fixed, reduced dimensions by adapting stochastic neighbor embedding (SNE) to…

In this paper, we present a novel error measure to compare a segmentation against ground truth. This measure, which we call Tolerant Edit Distance (TED), is motivated by two observations: (1) Some errors, like small boundary shifts, are…

Quantifying the degree of dissimilarity between two probability distributions on a finite metric space is a fundamental task in Computer Science and Computer Vision. A natural dissimilarity measure based on optimal transport is the Earth…

An elastic-degenerate string is a sequence of $n$ finite sets of strings of total length $N$, introduced to represent a set of related DNA sequences, also known as a pangenome. The ED string matching (EDSM) problem consists in reporting all…

Efficiently computing accurate representations of high-dimensional data is essential for data analysis and unsupervised learning. Dendrograms, also known as ultrametrics, are widely used representations that preserve hierarchical…

We consider the classic 1-center problem: Given a set $P$ of $n$ points in a metric space find the point in $P$ that minimizes the maximum distance to the other points of $P$. We study the complexity of this problem in $d$-dimensional…