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In the Shortest Common Superstring (SCS) problem, one is given a collection of strings, and needs to find a shortest string containing each of them as a substring. SCS admits $2\frac{11}{23}$-approximation in polynomial time (Mucha,…

Data Structures and Algorithms · Computer Science 2020-06-05 Alexander Golovnev , Alexander S. Kulikov , Alexander Logunov , Ivan Mihajlin , Maksim Nikolaev

The problem called "String reconstruction from substrings" is a mathematical model of sequencing by hybridization that plays an important role in DNA sequencing. In this problem, we are given a blackbox oracle holding an unknown string…

Data Structures and Algorithms · Computer Science 2018-08-03 Kazuo Iwama , Junichi Teruyama , Shuntaro Tsuyama

In this paper we consider the $p$-Norm Hamming Centroid problem which asks to determine whether some given binary strings have a centroid with a bound on the $p$-norm of its Hamming distances to the strings. Specifically, given a set of…

Computational Complexity · Computer Science 2019-06-28 Jiehua Chen , Danny Hermelin , Manuel Sorge

In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i.e., random subsequences of the…

Data Structures and Algorithms · Computer Science 2020-12-17 Sami Davies , Miklos Z. Racz , Cyrus Rashtchian , Benjamin G. Schiffer

We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of $n$ finite sets of strings of total length $N$, and compactly describes a collection of strings obtained by first…

Data Structures and Algorithms · Computer Science 2025-03-04 Paweł Gawrychowski , Adam Górkiewicz , Pola Marciniak , Solon P. Pissis , Karol Pokorski

Given a pattern string $P$ of length $n$ and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet of size $\Delta$, the {\em exact string matching} problem consists of finding all occurrences of…

Data Structures and Algorithms · Computer Science 2015-10-01 Srikrishnan Divakaran

In this paper we study the fundamental problem of maintaining a dynamic collection of strings under the following operations: concat - concatenates two strings, split - splits a string into two at a given position, compare - finds the…

Data Structures and Algorithms · Computer Science 2016-04-11 Paweł Gawrychowski , Adam Karczmarz , Tomasz Kociumaka , Jakub Łącki , Piotr Sankowski

We show that Closest Substring, one of the most important problems in the field of biological sequence analysis, is W[1]-hard when parameterized by the number k of input strings (and remains so, even over a binary alphabet). This problem is…

Computational Complexity · Computer Science 2007-05-23 Michael R. Fellows , Jens Gramm , Rolf Niedermeier

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

Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed…

Data Structures and Algorithms · Computer Science 2025-09-04 Philip Bille , Inge Li Gørtz , Simon J. Puglisi , Simon R. Tarnow

The Minimum Consistent Subset (MCS) problem arises naturally in the context of supervised clustering and instance selection. In supervised clustering, one aims to infer a meaningful partitioning of data using a small labeled subset.…

Data Structures and Algorithms · Computer Science 2025-12-16 Aritra Banik , Mano Prakash Parthasarathi , Venkatesh Raman , Diya Roy , Abhishek Sahu

A border of a string is a non-empty proper prefix of the string that is also a suffix. A string is unbordered if it has no border. The longest unbordered factor is a fundamental notion in stringology, closely related to string periodicity.…

Data Structures and Algorithms · Computer Science 2025-07-23 Shoma Sekizaki , Takuya Mieno

We report (to our knowledge) the first evaluation of Constraint Satisfaction as a computational framework for solving closest string problems. We show that careful consideration of symbol occurrences can provide search heuristics that…

Artificial Intelligence · Computer Science 2010-05-04 Tom Kelsey , Lars Kotthoff

The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…

Probability · Mathematics 2016-04-22 C. Houdré , H. Matzinger

The longest common extension (LCE) of two indices in a string is the length of the longest identical substrings starting at these two indices. The LCE problem asks to preprocess a string into a compact data structure that supports fast LCE…

Data Structures and Algorithms · Computer Science 2015-07-10 Philip Bille , Pawel Gawrychowski , Inge Li Goertz , Gad M. Landau , Oren Weimann

We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found…

Data Structures and Algorithms · Computer Science 2021-06-16 Karl Bringmann , Vincent Cohen-Addad , Debarati Das

Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the…

Genomics · Quantitative Biology 2009-11-10 Satya N. Majumdar , Sergei Nechaev

Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics over data mining to machine learning. Closing some gaps in the literature, we show that several fundamental problems in this…

Discrete Mathematics · Computer Science 2019-04-12 Laurent Bulteau , Vincent Froese , Rolf Niedermeier

We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give…

Data Structures and Algorithms · Computer Science 2018-02-20 Raphael Clifford , Allan Grønlund , Kasper Green Larsen , Tatiana Starikovskaya

Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…

Data Structures and Algorithms · Computer Science 2015-01-27 Atalay Mert İleri , M. Oğuzhan Külekci , Bojian Xu