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We present an algorithm for approximating the edit distance $\operatorname{ed}(x, y)$ between two strings $x$ and $y$ in time parameterized by the degree to which one of the strings $x$ satisfies a natural pseudorandomness property. The…

Data Structures and Algorithms · Computer Science 2018-11-13 William Kuszmaul

Given two strings of length $n$ over alphabet $\Sigma$, and an upper bound $k$ on their edit distance, the algorithm of Myers (Algorithmica'86) and Landau and Vishkin (JCSS'88) computes the unweighted string edit distance in…

Data Structures and Algorithms · Computer Science 2023-02-09 Debarati Das , Jacob Gilbert , MohammadTaghi Hajiaghayi , Tomasz Kociumaka , Barna Saha

Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. For example, edit distance of two strings of length $n$ can be solved in $O(n^2/w)$ time. In a reasonable…

Quantum Physics · Physics 2023-02-07 Massimo Equi , Arianne Meijer-van de Griend , Veli Mäkinen

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…

Data Structures and Algorithms · Computer Science 2021-12-14 Arun Ganesh , Tomasz Kociumaka , Andrea Lincoln , Barna Saha

The Swap-Insert Correction distance from a string $S$ of length $n$ to another string $L$ of length $m\geq n$ on the alphabet $[1..d]$ is the minimum number of insertions, and swaps of pairs of adjacent symbols, converting $S$ into $L$.…

Data Structures and Algorithms · Computer Science 2015-06-30 Jérémy Barbay , Pablo Pérez-Lantero

The tutorial describes the concept of edit distances applied to research and commercial contexts. We use Translation Edit Rate (TER), Levenshtein, Damerau-Levenshtein, Longest Common Subsequence and $n$-gram distances to demonstrate the…

Computation and Language · Computer Science 2024-10-10 Félix do Carmo , Diptesh Kanojia

The edit distance is a metric of dissimilarity between strings, widely applied in computational biology, speech recognition, and machine learning. Let $e_k(n)$ denote the average edit distance between random, independent strings of $n$…

Formal Languages and Automata Theory · Computer Science 2024-04-09 Gianfranco Bilardi , Michele Schimd

We study the problem of approximating the edit distance of two strings in sublinear time, in a setting where one or both string(s) are preprocessed, as initiated by Goldenberg, Rubinstein, Saha (STOC '20). Specifically, in the $(k, K)$-gap…

Data Structures and Algorithms · Computer Science 2022-10-13 Karl Bringmann , Alejandro Cassis , Nick Fischer , Vasileios Nakos

The problem of computing the edit-distance between a string and a finite automaton arises in a variety of applications in computational biology, text processing, and speech recognition. This paper presents linear-space algorithms for…

Formal Languages and Automata Theory · Computer Science 2009-04-30 Cyril Allauzen , Mehryar Mohri

We present the first dynamic algorithms for Dyck and tree edit distances with subpolynomial update times. Dyck edit distance measures how far a parenthesis string is from a well-parenthesized expression, while tree edit distance quantifies…

Data Structures and Algorithms · Computer Science 2025-10-21 Debarati Das , Jacob Gilbert , MohammadTaghi Hajiaghayi , Tomasz Kociumaka , Barna Saha

The edit distance $ed(X,Y)$ of two strings $X,Y\in \Sigma^*$ is the minimum number of character edits (insertions, deletions, and substitutions) needed to transform $X$ into $Y$. Its weighted counterpart $ed^w(X,Y)$ minimizes the total cost…

Data Structures and Algorithms · Computer Science 2025-07-04 Itai Boneh , Egor Gorbachev , Tomasz Kociumaka

The Median String Problem is W[1]-Hard under the Levenshtein distance, thus, approximation heuristics are used. Perturbation-based heuristics have been proved to be very competitive as regards the ratio approximation accuracy/convergence…

Data Structures and Algorithms · Computer Science 2020-03-05 Pedro Mirabal , José Abreu , Oscar Pedreira

In many applications, it is necessary to determine the string similarity. Edit distance[WF74] approach is a classic method to determine Field Similarity. A well known dynamic programming algorithm [GUS97] is used to calculate edit distance…

Data Structures and Algorithms · Computer Science 2007-05-23 Qi Xiao Yang , Sung Sam Yuan , Lu Chun , Li Zhao , Sun Peng

An edit distance is a measure of the minimum cost sequence of edit operations to transform one structure into another. Edit distance is most commonly encountered within the context of strings, where Wagner and Fischer's string edit distance…

Discrete Mathematics · Computer Science 2020-05-21 Vincent A. Cicirello

The tree edit distance is a natural dissimilarity measure between rooted ordered trees whose nodes are labeled over an alphabet $\Sigma$. It is defined as the minimum number of node edits (insertions, deletions, and relabelings) required to…

Data Structures and Algorithms · Computer Science 2025-07-04 Tomasz Kociumaka , Ali Shahali

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…

Data Structures and Algorithms · Computer Science 2020-05-04 Przemysław Uznański

Given a stream of items each associated with a numerical value, its edit distance to monotonicity is the minimum number of items to remove so that the remaining items are non-decreasing with respect to the numerical value. The space…

Data Structures and Algorithms · Computer Science 2011-11-24 Ho-Leung Chan , Tak-Wah Lam , Lap-Kei Lee , Jiangwei Pan , Hing-Fung Ting , Qin Zhang

There are efficient dynamic programming solutions to the computation of the Edit Distance from $S\in[1..\sigma]^n$ to $T\in[1..\sigma]^m$, for many natural subsets of edit operations, typically in time within $O(nm)$ in the worst-case over…

Information Retrieval · Computer Science 2018-06-13 Jérémy Barbay , Andrés Olivares

We present a unified framework for accelerating edit-distance computation between two compressible strings using straight-line programs. For two strings of total length $N$ having straight-line program representations of total size $n$, we…

Computational Complexity · Computer Science 2009-02-17 Danny Hermelin , Gad M. Landau , Shir Landau , Oren Weimann

Edit distance is an important measure of string similarity. It counts the number of insertions, deletions and substitutions one has to make to a string $x$ to get a string $y$. In this paper we design an almost linear-size sketching scheme…

Data Structures and Algorithms · Computer Science 2024-06-18 Michal Koucký , Michael Saks