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We study the problem of estimating the edit distance between two $n$-character strings. While exact computation in the worst case is believed to require near-quadratic time, previous work showed that in certain regimes it is possible to…

Data Structures and Algorithms · Computer Science 2020-07-29 Joshua Brakensiek , Moses Charikar , Aviad Rubinstein

In a way similar to the string-to-string correction problem we address time series similarity in the light of a time-series-to-time-series-correction problem for which the similarity between two time series is measured as the minimum cost…

Information Retrieval · Computer Science 2008-12-28 Pierre-François Marteau

The problem of finding the longest common subsequence (LCS) for a set of sequences is a very interesting and challenging problem in computer science. This problem is NP-complete, but because of its importance, many heuristic algorithms have…

Data Structures and Algorithms · Computer Science 2009-06-30 Kang Ning

The edit distance between two rooted ordered trees with $n$ nodes labeled from an alphabet~$\Sigma$ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling…

Data Structures and Algorithms · Computer Science 2017-03-28 Karl Bringmann , Paweł Gawrychowski , Shay Mozes , Oren Weimann

We study sublinear time algorithms for estimating the size of maximum matching. After a long line of research, the problem was finally settled by Behnezhad [FOCS'22], in the regime where one is willing to pay an approximation factor of $2$.…

Data Structures and Algorithms · Computer Science 2023-04-28 Sayan Bhattacharya , Peter Kiss , Thatchaphol Saranurak

We give the first $2$-approximation algorithm for the cluster vertex deletion problem. This is tight, since approximating the problem within any constant factor smaller than $2$ is UGC-hard. Our algorithm combines the previous approaches,…

Combinatorics · Mathematics 2021-10-19 Manuel Aprile , Matthew Drescher , Samuel Fiorini , Tony Huynh

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

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

This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common…

Data Structures and Algorithms · Computer Science 2016-08-26 Daxin Zhu , Lei Wang , Tinran Wang , Xiaodong Wang

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

Approximate Pattern Matching is among the most fundamental string-processing tasks. Given a text $T$ of length $n$, a pattern $P$ of length $m$, and a threshold $k$, the task is to identify the fragments of $T$ that are at distance at most…

Data Structures and Algorithms · Computer Science 2024-10-10 Tomasz Kociumaka , Jakob Nogler , Philip Wellnitz

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

We introduce a novel definition of approximate palindromes in strings, and provide an algorithm to find all maximal approximate palindromes in a string with up to $k$ errors. Our definition is based on the usual edit operations of…

Data Structures and Algorithms · Computer Science 2007-05-23 A. H. L. Porto , V. C. Barbosa

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

In this paper, we design new sublinear-time algorithms for solving the gap edit distance problem and for embedding edit distance to Hamming distance. For the gap edit distance problem, we give an $\tilde{O}(\frac{n}{k}+k^2)$-time greedy…

Data Structures and Algorithms · Computer Science 2020-11-17 Tomasz Kociumaka , Barna Saha

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

In this work, we consider a variant of the classical Longest Common Subsequence problem called Doubly-Constrained Longest Common Subsequence (DC-LCS). Given two strings s1 and s2 over an alphabet A, a set C_s of strings, and a function Co…

Data Structures and Algorithms · Computer Science 2013-11-20 Paola Bonizzoni , Gianluca Della Vedova , Riccardo Dondi , Yuri Pirola

Although several self-indexes for highly repetitive text collections exist, developing an index and search algorithm with editing operations remains a challenge. Edit distance with moves (EDM) is a string-to-string distance measure that…

Data Structures and Algorithms · Computer Science 2016-04-11 Yoshimasa Takabatake , Kenta Nakashima , Tetsuji Kuboyama , Yasuo Tabei , Hiroshi Sakamoto

Consider two random strings having the same length and generated by an iid sequence taking its values uniformly in a fixed finite alphabet. Artificially place a long constant block into one of the strings, where a constant block is a…

Probability · Mathematics 2014-01-31 S. Amsalu , C. Houdré , H. Matzinger

A recent and active line of work achieves tight lower bounds for fundamental problems under the Strong Exponential Time Hypothesis (SETH). A celebrated result of Backurs and Indyk (STOC'15) proves that the Edit Distance of two sequences of…

Computational Complexity · Computer Science 2015-11-20 Amir Abboud , Thomas Dueholm Hansen , Virginia Vassilevska Williams , Ryan Williams