相关论文: Edit distance in substitution systems

For any $T \geq 1$, there are constants $R=R(T) \geq 1$ and $\zeta=\zeta(T)>0$ and a randomized algorithm that takes as input an integer $n$ and two strings $x,y$ of length at most $n$, and runs in time $O(n^{1+\frac{1}{T}})$ and outputs an…

The deviation of the observed frequency of a word $w$ from its expected frequency in a given sequence $x$ is used to determine whether or not the word is avoided. This concept is particularly useful in DNA linguistic analysis. The value of…

This paper addresses the problem of determining the distance between two regular languages. It will show how to expand Jaccard distance, which works on finite sets, to potentially-infinite regular languages. The entropy of a regular…

A word is called carefully synchronising for a partial deterministic finite semi-automaton if it maps all states to the same state. Equivalently, it is a composition of partial transformations equal to a constant total transformation. There…

The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…

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…

As it follows from the theory of almost periodic functions the set of integer solutions $q$ to the Kronecker system $|\omega_{j} q - \theta_{j}| < \varepsilon \pmod 1$, $j=1,\ldots,m$, where $1,\omega_{1},\ldots,\omega_{m}$ are linearly…

Dynamic time warping distance (DTW) is a widely used distance measure between time series $x, y \in \Sigma^n$. It was shown by Abboud, Backurs, and Williams that in the \emph{binary case}, where $|\Sigma| = 2$, DTW can be computed in time…

Classic similarity measures of strings are longest common subsequence and Levenshtein distance (i.e., the classic edit distance). A classic similarity measure of curves is dynamic time warping. These measures can be computed by simple…

The rank and select operations over a string of length n from an alphabet of size $\sigma$ have been used widely in the design of succinct data structures. In many applications, the string itself need be maintained dynamically, allowing…

In this paper, we establish that the maximum edit distance of an $n$-vertex graph from the hereditary property of word-representable graphs is $n^2/8-o(n^2)$. In addition, we establish that the maximum edit distance of an $n$-vertex graph…

We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the…

The $S$-gap shifts have a dynamically and combinatorially rich structure. Dynamical properties of the $S$-gap shift can be related to the properties of the set $S$. This interplay is particularly interesting when $S$ is not syndetic such as…

It is shown that for finding rational approximates to m'th root of any integer to any accuracy one only needs the ability to count and to distinguish between m different classes of objects. To every integer N can be associated a…

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 formula complexity of the word problem $\mathsf{Word}_{S_n,k} : \{0,1\}^{kn^2} \to \{0,1\}$: given $n$-by-$n$ permutation matrices $M_1,\dots,M_k$, compute the $(1,1)$-entry of the matrix product $M_1\cdots M_k$. An important…

$\newcommand{\Re}{\mathbb{R}}$We study the minWSPD problem of computing the minimum-size well-separated pairs decomposition of a set of points, and show constant approximation algorithms in low-dimensional Euclidean space and doubling…

The Dynamic Time Warping (DTW) distance is a popular measure of similarity for a variety of sequence data. For comparing polygonal curves $\pi, \sigma$ in $\mathbb{R}^d$, it provides a robust, outlier-insensitive alternative to the…

Real-world data often comes in compressed form. Analyzing compressed data directly (without decompressing it) can save space and time by orders of magnitude. In this work, we focus on fundamental sequence comparison problems and try to…

Gap Hamming Distance is a well-studied problem in communication complexity, in which Alice and Bob have to decide whether the Hamming distance between their respective n-bit inputs is less than n/2-sqrt(n) or greater than n/2+sqrt(n). We…