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The problem of aligning two strings A,B in order to determine their similarity is fundamental in the field of pattern matching. An important concept in this domain is the "all scores matrix" that encodes the local alignment comparison of…

Data Structures and Algorithms · Computer Science 2018-08-13 Amir Carmel , Dekel Tsur , Michal Ziv-Ukelson

The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings $S$…

Data Structures and Algorithms · Computer Science 2026-04-09 Panagiotis Charalampopoulos , Paweł Gawrychowski , Karol Pokorski

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 problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…

Data Structures and Algorithms · Computer Science 2008-07-29 Dimitris Papamichail , Georgios Papamichail

In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $O(\sigma~ n^2)$ time algorithm, where $n$ is the length of the strings and $\sigma$ is the alphabet…

Data Structures and Algorithms · Computer Science 2015-03-03 Ali Alatabbi , Costas S. Iliopoulos , Alessio Langiu , M. Sohel Rahman

The Longest Common Subsequence Problem (LCS) deals with finding the longest subsequence among a given set of strings. The LCS problem is an NP-hard problem which makes it a target for lots of effort to find a better solution with heuristics…

Data Structures and Algorithms · Computer Science 2022-06-24 Alireza Abdi , Mohsen Hooshmand

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

We give a sublinear quantum algorithm for the longest common substring (LCS) problem on the run-length encoded (RLE) inputs, under the assumption that the prefix-sums of the runs are given. Our algorithm costs $\tilde{O}(n^{5/6})\cdot…

Quantum Physics · Physics 2023-10-03 Tzu-Ching Lee , Han-Hsuan Lin

Given a string $S$ of $n$ symbols, a longest common extension query $\mathsf{LCE}(i,j)$ asks for the length of the longest common prefix of the $i$th and $j$th suffixes of $S$. LCE queries have several important applications in string…

Data Structures and Algorithms · Computer Science 2016-02-01 Yuka Tanimura , Tomohiro I , Hideo Bannai , Shunsuke Inenaga , Simon J. Puglisi , Masayuki Takeda

We provide a deterministic algorithm that outputs an $O(n^{3/4} \log n)$-approximation for the Longest Common Subsequence (LCS) of two input sequences of length $n$ in near-linear time. This is the first deterministic approximation…

Data Structures and Algorithms · Computer Science 2025-07-31 Itai Boneh , Shay Golan , Matan Kraus

Random access to highly compressed strings -- represented by straight-line programs or Lempel-Ziv parses, for example -- is a well-studied topic. Random access to such strings in strongly sublogarithmic time is impossible in the worst case,…

Data Structures and Algorithms · Computer Science 2026-02-05 Ferdinando Cicalese , Zsuzsanna Lipták , Travis Gagie , Gonzalo Navarro , Nicola Prezza , Cristian Urbina

The recently introduced longest common substring with $k$-mismatches ($k$-LCF) problem is to find, given two sequences $S_1$ and $S_2$ of length $n$ each, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance…

Data Structures and Algorithms · Computer Science 2014-10-15 Szymon Grabowski

We present an algorithm computing the longest periodic subsequence of a string of length $n$ in $O(n^7)$ time with $O(n^4)$ words of space. We obtain improvements when restricting the exponents or extending the search allowing the reported…

Data Structures and Algorithms · Computer Science 2022-02-16 Hideo Bannai , Tomohiro I , Dominik Köppl

We revisit the longest common extension (LCE) problem, that is, preprocess a string $T$ into a compact data structure that supports fast LCE queries. An LCE query takes a pair $(i,j)$ of indices in $T$ and returns the length of the longest…

Data Structures and Algorithms · Computer Science 2013-04-23 Philip Bille , Inge Li Goertz , Benjamin Sach , Hjalte Wedel Vildhøj

The longest common substring with $k$-mismatches problem is to find, given two strings $S_1$ and $S_2$, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ and $A_2$ is $\le k$. We introduce a…

Data Structures and Algorithms · Computer Science 2015-04-08 Tomas Flouri , Emanuele Giaquinta , Kassian Kobert , Esko Ukkonen

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

This paper gives new results for synchronization strings, a powerful combinatorial object that allows to efficiently deal with insertions and deletions in various communication settings: $\bullet$ We give a deterministic, linear time…

Information Theory · Computer Science 2017-11-13 Bernhard Haeupler , Amirbehshad Shahrasbi

Two strings of the same length are said to Cartesian-tree match (CT-match) if their Cartesian-trees are isomorphic [Park et al., TCS 2020]. Cartesian-tree matching is a natural model that allows for capturing similarities of numerical…

Data Structures and Algorithms · Computer Science 2026-01-01 Taketo Tsujimoto , Yuki Yonemoto , Hiroki Shibata , Takuya Mieno , Yuto Nakashima , Shunsuke Inenaga

Non-parametric entropy estimation on sequential data is a fundamental tool in signal processing, capturing information flow within or between processes to measure predictability, redundancy, or similarity. Methods based on longest common…

Data Structures and Algorithms · Computer Science 2025-10-16 Bridget Smart , Max Ward , Matthew Roughan

Motivated by computing duplication patterns in sequences, a new fundamental problem called the longest subsequence-repeated subsequence (LSRS) is proposed. Given a sequence $S$ of length $n$, a letter-repeated subsequence is a subsequence…

Data Structures and Algorithms · Computer Science 2023-09-01 Manuel Lafond , Wenfeng Lai , Adiesha Liyanage , Binhai Zhu