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The edit distance is a basic string similarity measure used in many applications such as text mining, signal processing, bioinformatics, and so on. However, the computational cost can be a problem when we repeat many distance calculations…

Data Structures and Algorithms · Computer Science 2017-01-24 Hiroyuki Hanada , Mineichi Kudo , Atsuyoshi Nakamura

We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-approximation for ED and a…

Data Structures and Algorithms · Computer Science 2026-04-01 Xiao Mao , Aviad Rubinstein

The edit distance problem is a classical fundamental problem in computer science in general, and in combinatorial pattern matching in particular. The standard dynamic programming solution for this problem computes the edit-distance between…

Data Structures and Algorithms · Computer Science 2016-10-05 Danny Hermelin , Gad M. Landau , Shir Landau , Oren Weimann

Several measures exist for string similarity, including notable ones like the edit distance and the indel distance. The former measures the count of insertions, deletions, and substitutions required to transform one string into another,…

Data Structures and Algorithms · Computer Science 2024-10-15 Sudatta Bhattacharya , Sanjana Dey , Elazar Goldenberg , Michal Koucký

We consider the following model for sampling pairs of strings: $s_1$ is a uniformly random bitstring of length $n$, and $s_2$ is the bitstring arrived at by applying substitutions, insertions, and deletions to each bit of $s_1$ with some…

Data Structures and Algorithms · Computer Science 2020-07-08 Arun Ganesh , Aaron Sy

Classically, the edit distance of two length-$n$ strings can be computed in $O(n^2)$ time, whereas an $O(n^{2-\epsilon})$-time procedure would falsify the Orthogonal Vectors Hypothesis. If the edit distance does not exceed $k$, the running…

Data Structures and Algorithms · Computer Science 2023-11-06 Daniel Gibney , Ce Jin , Tomasz Kociumaka , Sharma V. Thankachan

Computing the edit distance of two strings is one of the most basic problems in computer science and combinatorial optimization. Tree edit distance is a natural generalization of edit distance in which the task is to compute a measure of…

Data Structures and Algorithms · Computer Science 2022-09-16 Debarati Das , Jacob Gilbert , MohammadTaghi Hajiaghayi , Tomasz Kociumaka , Barna Saha , Hamed Saleh

We revisit the problem of computing the edit distance of a regular language given via an NFA. This problem relates to the inherent maximal error-detecting capability of the language in question. We present an efficient algorithm for solving…

Formal Languages and Automata Theory · Computer Science 2014-06-05 Lila Kari , Stavros Konstantinidis , Steffen Kopecki , Meng Yang

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

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…

Data Structures and Algorithms · Computer Science 2018-11-06 Diptarka Chakraborty , Debarati Das , Michal Koucky

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

We revisit the task of computing the edit distance in sublinear time. In the $(k,K)$-gap edit distance problem the task is to distinguish whether the edit distance of two strings is at most $k$ or at least $K$. It has been established by…

Data Structures and Algorithms · Computer Science 2023-03-17 Karl Bringmann , Alejandro Cassis , Nick Fischer , Vasileios Nakos

The normalized edit distance is one of the distances derived from the edit distance. It is useful in some applications because it takes into account the lengths of the two strings compared. The normalized edit distance is not defined in…

Neural and Evolutionary Computing · Computer Science 2013-12-09 Muhammad Marwan Muhammad Fuad

The Dyck language, which consists of well-balanced sequences of parentheses, is one of the most fundamental context-free languages. The Dyck edit distance quantifies the number of edits (character insertions, deletions, and substitutions)…

Data Structures and Algorithms · Computer Science 2021-12-14 Debarati Das , Tomasz Kociumaka , Barna Saha

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

We show that the edit distance between two run-length encoded strings of compressed lengths $m$ and $n$ respectively, can be computed in $\mathcal{O}(mn\log(mn))$ time. This improves the previous record by a factor of…

Data Structures and Algorithms · Computer Science 2019-05-06 Raphaël Clifford , Paweł Gawrychowski , Tomasz Kociumaka , Daniel P. Martin , Przemysław Uznański

The edit distance (ED) and longest common subsequence (LCS) are two fundamental problems which quantify how similar two strings are to one another. In this paper, we consider these problems in the asymmetric streaming model introduced by…

Data Structures and Algorithms · Computer Science 2020-04-17 Alireza Farhadi , MohammadTaghi Hajiaghayi , Aviad Rubinstein , Saeed Seddighin

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

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

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