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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

The edit distance is a way of quantifying how similar two strings are to one another by counting the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. In this paper we…

Data Structures and Algorithms · Computer Science 2016-07-14 Diptarka Chakraborty , Elazar Goldenberg , Michal Koucký

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

We consider integer programming problems in standard form $\max \{c^Tx : Ax = b, \, x\geq 0, \, x \in Z^n\}$ where $A \in Z^{m \times n}$, $b \in Z^m$ and $c \in Z^n$. We show that such an integer program can be solved in time $(m…

Discrete Mathematics · Computer Science 2019-06-10 Friedrich Eisenbrand , Robert Weismantel

We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an…

Information Theory · Computer Science 2021-03-16 Jon-Lark Kim , Young-Hun Kim , Nari Lee

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

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

In this paper we define a new problem, motivated by computational biology, $LCSk$ aiming at finding the maximal number of $k$ length $substrings$, matching in both input strings while preserving their order of appearance. The traditional…

Data Structures and Algorithms · Computer Science 2014-02-11 Gary Benson , Avivit Levy , Riva Shalom

We present an algorithm for approximating the edit distance between two strings of length $n$ in time $n^{1+\varepsilon}$ up to a constant factor, for any $\varepsilon>0$. Our result completes a research direction set forth in the recent…

Data Structures and Algorithms · Computer Science 2022-07-18 Alexandr Andoni , Negev Shekel Nosatzki

The edit distance between two strings is defined as the smallest number of insertions, deletions, and substitutions that need to be made to transform one of the strings to another one. Approximating edit distance in subquadratic time is…

Data Structures and Algorithms · Computer Science 2018-04-27 Mahdi Boroujeni , Soheil Ehsani , Mohammad Ghodsi , MohammadTaghi HajiAghayi , Saeed Seddighin

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

We study the fundamental problem of approximating the edit distance of two strings. After an extensive line of research led to the development of a constant-factor approximation algorithm in almost-linear time, recent years have witnessed a…

Data Structures and Algorithms · Computer Science 2023-12-05 Karl Bringmann , Alejandro Cassis , Nick Fischer , Tomasz Kociumaka

The edit distance of two strings is the minimum number of insertions, deletions, and substitutions needed to transform one string into the other. The textbook algorithm determines the edit distance of length-$n$ strings in $O(n^2)$ time,…

Data Structures and Algorithms · Computer Science 2025-02-04 Egor Gorbachev , Tomasz Kociumaka

We show how to compute the edit distance between two strings of length n up to a factor of 2^{\~O(sqrt(log n))} in n^(1+o(1)) time. This is the first sub-polynomial approximation algorithm for this problem that runs in near-linear time,…

Data Structures and Algorithms · Computer Science 2011-09-27 Alexandr Andoni , Krzysztof Onak

Edit distance is a fundamental measure of distance between strings and has been widely studied in computer science. While the problem of estimating edit distance has been studied extensively, the equally important question of actually…

Data Structures and Algorithms · Computer Science 2018-05-08 Moses Charikar , Ofir Geri , Michael P. Kim , William Kuszmaul

Suppose that we have two parties that possess each a binary string. Suppose that the length of the first string (document) is $n$ and that the two strings (documents) have edit distance (minimal number of deletes, inserts and substitutions…

Data Structures and Algorithms · Computer Science 2015-12-04 Djamal Belazzougui

Under polynomial time reduction, the maximum likelihood decoding of a linear code is equivalent to computing the error distance of a received word. It is known that the decoding complexity of standard Reed-Solomon codes at certain radius is…

Number Theory · Mathematics 2015-08-13 Li Yujuan , Zhu Guizhen

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…

Data Structures and Algorithms · Computer Science 2020-01-03 Timothy M. Chan , Shay Golan , Tomasz Kociumaka , Tsvi Kopelowitz , Ely Porat

This paper introduces the notion of exact common information, which is the minimum description length of the common randomness needed for the exact distributed generation of two correlated random variables $(X,Y)$. We introduce the quantity…

Information Theory · Computer Science 2014-02-04 Gowtham Ramani Kumar , Cheuk Ting Li , Abbas El Gamal

Given a context free language $\mathcal{L(G)}$ over alphabet $\Sigma$ and a string $s \in \Sigma^*$, {\em the language edit distance} problem seeks the minimum number of edits (insertions, deletions and substitutions) required to convert…

Data Structures and Algorithms · Computer Science 2024-10-25 Tomasz Kociumaka , Barna Saha