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The {\em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. LCS is a central problem in stringology and finds broad applications in text compression, error-detecting codes and biological…

Data Structures and Algorithms · Computer Science 2010-04-20 Shihabur Rahman Chowdhury , Masud Hasan , Sumaiya Iqbal , M. Sohel Rahman

Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…

Data Structures and Algorithms · Computer Science 2025-09-22 Hamed Hasibi , Neerja Mhaskar , W. F. Smyth

In this paper we provide a new locally consistent decomposition of strings. Each string $x$ is decomposed into blocks that can be described by grammars of size $\widetilde{O}(k)$ (using some amount of randomness). If we take two strings $x$…

Data Structures and Algorithms · Computer Science 2023-11-28 Sudatta Bhattacharya , Michal Koucký

Given a pair of strings, the problems of computing their Longest Common Subsequence and Edit Distance have been extensively studied for decades. For exact algorithms, LCS and Edit Distance (with character insertions and deletions) are…

Data Structures and Algorithms · Computer Science 2019-04-12 Aviad Rubinstein , Zhao Song

The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings $A$ and $B$. More recently, a set of four constrained LCS problems (called generalized…

Data Structures and Algorithms · Computer Science 2020-01-17 Kohei Yamada , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda

This study develops an algorithm to solve a variation of the Shortest Common Superstring (SCS) problem. There are two modifications to the base SCS problem. First, one string in the set S is allowed to have up to K mistakes, defined as not…

Data Structures and Algorithms · Computer Science 2024-11-05 Arthur Gilfanov

We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a…

Data Structures and Algorithms · Computer Science 2023-07-21 Miyuji Hirota , Yoshifumi Sakai

In this paper, we study for the first time the Diverse Longest Common Subsequences (LCSs) problem under Hamming distance. Given a set of a constant number of input strings, the problem asks to decide if there exists some subset $\mathcal X$…

Data Structures and Algorithms · Computer Science 2024-06-12 Yuto Shida , Giulia Punzi , Yasuaki Kobayashi , Takeaki Uno , Hiroki Arimura

The problem of finding longest common subsequence (LCS) is one of the fundamental problems in computer science, which finds application in fields such as computational biology, text processing, information retrieval, data compression etc.…

Computational Complexity · Computer Science 2020-06-25 Amey Bhangale , Diptarka Chakraborty , Rajendra Kumar

The problem of determining the correct order of fluctuation of the optimal alignment score of two random strings of length $n$ has been open for several decades. It is known that the biased expected effect of a random letter-change on the…

Probability · Mathematics 2012-11-26 Saba Amsalu , Raphael Hauser , Heinrich Matzinger

Algorithms to find optimal alignments among strings, or to find a parsimonious summary of a collection of strings, are well studied in a variety of contexts, addressing a wide range of interesting applications. In this paper, we consider…

Social and Information Networks · Computer Science 2020-11-09 Patty Commins , David Liben-Nowell , Tina Liu , Kiran Tomlinson

Considering two optimally aligned random sequences, we investigate the effect on the alignment score caused by changing a random letter in one of the two sequences. Using this idea in conjunction with large deviations theory, we show that…

Probability · Mathematics 2015-06-15 Raphael Hauser , Heinrich Matzinger

Longest Common Substring (LCS) is an important text processing problem, which has recently been investigated in the quantum query model. The decisional version of this problem, LCS with threshold $d$, asks whether two length-$n$ input…

Data Structures and Algorithms · Computer Science 2022-11-30 Ce Jin , Jakob Nogler

The problem of finding a longest common subsequence of two main sequences with some constraint that must be a substring of the result (STR-IC-LCS) was formulated recently. It is a variant of the constrained longest common subsequence…

Data Structures and Algorithms · Computer Science 2011-07-01 Sebastian Deorowicz

We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…

Information Theory · Computer Science 2021-11-24 Anina Gruica , Alberto Ravagnani

Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…

Data Structures and Algorithms · Computer Science 2025-04-08 Giovanni Buzzega , Alessio Conte , Yasuaki Kobayashi , Kazuhiro Kurita , Giulia Punzi

When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…

Combinatorics · Mathematics 2023-06-22 Yonah Biers-Ariel , Anant Godbole , Elizabeth Kelley

In many real-world database systems, a large fraction of the data is represented by strings: sequences of letters over some alphabet. This is because strings can easily encode data arising from different sources. It is often crucial to…

Data Structures and Algorithms · Computer Science 2024-07-17 Lorraine A. K. Ayad , Grigorios Loukides , Solon P. Pissis

We consider the problem of estimating the probability of an observed string drawn i.i.d. from an unknown distribution. The key feature of our study is that the length of the observed string is assumed to be of the same order as the size of…

Information Theory · Computer Science 2007-07-13 Aaron B. Wagner , Pramod Viswanath , Sanjeev R. Kulkarni

In the longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, and we are asked to find a longest string occurring as a fragment of both $S$ and $T$. This is a classical and well-studied…

Data Structures and Algorithms · Computer Science 2018-07-17 Amihood Amir , Panagiotis Charalampopoulos , Solon P. Pissis , Jakub Radoszewski