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Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…

Quantum Physics · Physics 2025-10-20 Josh Cudby , Sergii Strelchuk

Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…

Data Structures and Algorithms · Computer Science 2010-07-15 John Byers , Brent Heeringa , Michael Mitzenmacher , Georgios Zervas

This paper investigates the approximability of the Longest Common Subsequence (LCS) problem. The fastest algorithm for solving the LCS problem exactly runs in essentially quadratic time in the length of the input, and it is known that under…

Data Structures and Algorithms · Computer Science 2021-05-10 Shyan Akmal , Virginia Vassilevska Williams

We study the linearizability monitoring problem, which asks whether a given concurrent history of a data structure is equivalent to some sequential execution of the same data structure. In general, this problem is $\textsf{NP}$-hard, even…

Programming Languages · Computer Science 2026-05-26 Lee Zheng Han , Umang Mathur

The Shortest Superstring Problem (SSP) consists, for a set of strings S = {s_1,...,s_n}, to find a minimum length string that contains all s_i, 1 <= i <= k, as substrings. This problem is proved to be NP-Complete and APX-hard. Guaranteed…

Discrete Mathematics · Computer Science 2016-05-19 Tristan Braquelaire , Marie Gasparoux , Mathieu Raffinot , Raluca Uricaru

Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences…

Data Structures and Algorithms · Computer Science 2013-11-20 Sebastian Deorowicz , Szymon Grabowski

Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…

Data Structures and Algorithms · Computer Science 2011-11-10 Alexander Tiskin

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

Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works…

Genomics · Quantitative Biology 2023-11-21 Yue Wang

The longest run subsequence (LRS) problem is an NP-hard combinatorial optimization problem belonging to the class of subsequence problems from bioinformatics. In particular, the problem plays a role in genome reassembly. In this paper, we…

Artificial Intelligence · Computer Science 2025-08-20 Christian Blum , Pedro Pinacho-Davidson

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

We give a new characterization of maximal repetitions (or runs) in strings based on Lyndon words. The characterization leads to a proof of what was known as the "runs" conjecture (Kolpakov \& Kucherov (FOCS '99)), which states that the…

Discrete Mathematics · Computer Science 2018-07-03 Hideo Bannai , Tomohiro I , Shunsuke Inenaga , Yuto Nakashima , Masayuki Takeda , Kazuya Tsuruta

This study investigates whether reoptimization can help in solving the closest substring problem. We are dealing with the following reoptimization scenario. Suppose, we have an optimal l-length closest substring of a given set of sequences…

Data Structures and Algorithms · Computer Science 2017-03-21 Jhoirene B. Clemente , Henry N. Adorna

In this paper, we consider two versions of the Text Assembling problem. We are given a sequence of strings $s^1,\dots,s^n$ of total length $L$ that is a dictionary, and a string $t$ of length $m$ that is texts. The first version of the…

Quantum Physics · Physics 2024-04-05 Kamil Khadiev , Carlos Manuel Bosch Machado , Zeyu Chen , Junde Wu

We consider the general problem of the Longest Common Subsequence (LCS) on weighted sequences. Weighted sequences are an extension of classical strings, where in each position every letter of the alphabet may occur with some probability.…

Computational Complexity · Computer Science 2020-07-21 Evangelos Kipouridis , Kostas Tsichlas

Repeat finding in strings has important applications in subfields such as computational biology. The challenge of finding the longest repeats covering particular string positions was recently proposed and solved by \.{I}leri et al., using a…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-01-28 Yun Tian , Bojian Xu

This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…

Discrete Mathematics · Computer Science 2007-05-23 Ronald I. Greenberg

In this paper, we consider a generalized longest common subsequence problem, the string-excluding constrained LCS problem. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a constraint string $P$ of length $r$, the…

Data Structures and Algorithms · Computer Science 2013-01-31 Lei Wang , Xiaodong Wang , Yingjie Wu , Daxin Zhu

Block Sorting is a well studied problem, motivated by its applications in Optical Character Recognition (OCR), and Computational Biology. Block Sorting has been shown to be NP-Hard, and two separate polynomial time 2-approximation…

Computational Complexity · Computer Science 2011-10-06 N. S. Narayanaswamy , Swapnoneel Roy

A tandem duplication denotes the process of inserting a copy of a segment of DNA adjacent to its original position. More formally, a tandem duplication can be thought of as an operation that converts a string $S = AXB$ into a string $T =…

Computational Complexity · Computer Science 2021-03-16 Ferdinando Cicalese , Nicolò Pilati