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In this paper we are interested in indexing texts for substring matching queries with one edit error. That is, given a text $T$ of $n$ characters over an alphabet of size $\sigma$, we are asked to build a data structure that answers the…

Data Structures and Algorithms · Computer Science 2014-08-25 Djamal Belazzougui

In the trace reconstruction problem, the goal is to reconstruct an unknown string $x$ of length $n$ from multiple traces obtained by passing $x$ through the deletion channel. In the relaxed problem of $approximate$ trace reconstruction, the…

Probability · Mathematics 2021-07-15 Zachary Chase , Yuval Peres

Edit-distance-based string similarity search has many applications such as spell correction, data de-duplication, and sequence alignment. However, computing edit distance is known to have high complexity, which makes string similarity…

Databases · Computer Science 2020-05-25 Xinyan Dai , Xiao Yan , Kaiwen Zhou , Yuxuan Wang , Han Yang , James Cheng

In the longest common substring problem, we are given two strings of length $n$ and must find a substring of maximal length that occurs in both strings. It is well known that the problem can be solved in linear time, but the solution is not…

Data Structures and Algorithms · Computer Science 2018-08-21 Tomasz Kociumaka , Jakub Radoszewski , Tatiana Starikovskaya

Hairpin completion, derived from the hairpin formation observed in DNA biochemistry, is an operation applied to strings, particularly useful in DNA computing. Conceptually, a right hairpin completion operation transforms a string $S$ into…

Data Structures and Algorithms · Computer Science 2024-04-19 Itai Boneh , Dvir Fried , Shay Golan , Matan Kraus

An edge-operation on a graph $G$ is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs $\mathcal{G}$, the editing distance from $G$ to $\mathcal{G}$ is the smallest number…

Combinatorics · Mathematics 2016-05-24 Maria Axenovich , André Kézdy , Ryan R. Martin

A measure of similarity between text embeddings can be considered adequate only if it adheres to the human perception of similarity between texts. In this paper, we introduce the distance-to-distance ratio (DDR), a novel measure of…

Computation and Language · Computer Science 2026-01-27 Abdullah Qureshi , Kenneth Rice , Alexander Wolpert

String consensus problems aim at finding a string that minimizes some given distance with respect to an input set of strings. In particular, in the Closest string problem, we are given a set of strings of equal length and a radius $d$. The…

Data Structures and Algorithms · Computer Science 2025-07-29 Estéban Gabory , Laurent Bulteau , Gabriele Fici , Hilde Verbeek

Political scientists often find themselves tracking amendments to political texts. As different actors weigh in, texts change as they are drafted and redrafted, reflecting political preferences and power. This study provides a novel…

Computation and Language · Computer Science 2016-08-24 Henrik Hermansson , James P. Cross

We consider an \emph{approximate} version of the trace reconstruction problem, where the goal is to recover an unknown string $s\in\{0,1\}^n$ from $m$ traces (each trace is generated independently by passing $s$ through a probabilistic…

Data Structures and Algorithms · Computer Science 2021-07-21 Diptarka Chakraborty , Debarati Das , Robert Krauthgamer

Edit distance with moves (EDM) is a string-to-string distance measure that includes substring moves in addition to ordinal editing operations to turn one string to the other. Although optimizing EDM is intractable, it has many applications…

Data Structures and Algorithms · Computer Science 2014-08-27 Yoshimasa Takabatake , Yasuo Tabei , Hiroshi Sakamoto

In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…

Data Structures and Algorithms · Computer Science 2021-05-12 Tatsuya Akutsu , Tomoya Mori , Naotoshi Nakamura , Satoshi Kozawa , Yuhei Ueno , Thomas N. Sato

The Earth Mover's Distance is a popular similarity measure in several branches of computer science. It measures the minimum total edge length of a perfect matching between two point sets. The Earth Mover's Distance under Translation…

Computational Geometry · Computer Science 2025-11-18 Karl Bringmann , Frank Staals , Karol Węgrzycki , Geert van Wordragen

The Fr\'echet distance is a popular measure of dissimilarity for polygonal curves. It is defined as a min-max formulation that considers all direction-preserving continuous bijections of the two curves. Because of its susceptibility to…

Computational Geometry · Computer Science 2022-02-24 Jacobus Conradi , Anne Driemel

We propose the neural string edit distance model for string-pair matching and string transduction based on learnable string edit distance. We modify the original expectation-maximization learned edit distance algorithm into a differentiable…

Computation and Language · Computer Science 2022-04-28 Jindřich Libovický , Alexander Fraser

We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…

Data Structures and Algorithms · Computer Science 2021-10-22 Shyan Akmal , Ce Jin

An elastic-degenerate (ED) string $T$ is a sequence of $n$ sets $T[1],\ldots,T[n]$ containing $m$ strings in total whose cumulative length is $N$. We call $n$, $m$, and $N$ the length, the cardinality and the size of $T$, respectively. The…

Data Structures and Algorithms · Computer Science 2024-11-13 Esteban Gabory , Moses Njagi Mwaniki , Nadia Pisanti , Solon P. Pissis , Jakub Radoszewski , Michelle Sweering , Wiktor Zuba

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…

Data Structures and Algorithms · Computer Science 2011-03-21 Philip Bille

We study the problem of computing the Fr\'echet distance between two polygonal curves under transformations. First, we consider translations in the Euclidean plane. Given two curves $\pi$ and $\sigma$ of total complexity $n$ and a threshold…

Computational Geometry · Computer Science 2025-01-23 Kevin Buchin , Maike Buchin , Zijin Huang , André Nusser , Sampson Wong

We study the document exchange problem under multiple substring edits. A substring edit in a string $\mathbf{x}$ occurs when a substring $\mathbf{u}$ of $\mathbf{x}$ is replaced by an arbitrary string $\mathbf{v}$. The lengths of…

Information Theory · Computer Science 2026-01-27 Hrishi Narayanan , Vinayak Ramkumar , Rawad Bitar , Antonia Wachter-Zeh