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Minimizers sampling is one of the most widely-used mechanisms for sampling strings [Roberts et al., Bioinformatics 2004]. Let $S=S[1]\ldots S[n]$ be a string over a totally ordered alphabet $\Sigma$. Further let $w\geq 2$ and $k\geq 1$ be…

Data Structures and Algorithms · Computer Science 2024-05-08 Hilde Verbeek , Lorraine A. K. Ayad , Grigorios Loukides , Solon P. Pissis

The Swap-Insert Correction distance from a string $S$ of length $n$ to another string $L$ of length $m\geq n$ on the alphabet $[1..d]$ is the minimum number of insertions, and swaps of pairs of adjacent symbols, converting $S$ into $L$.…

Data Structures and Algorithms · Computer Science 2015-06-30 Jérémy Barbay , Pablo Pérez-Lantero

In the k-mappability problem, we are given a string x of length n and integers m and k, and we are asked to count, for each length-m factor y of x, the number of other factors of length m of x that are at Hamming distance at most k from y.…

Data Structures and Algorithms · Computer Science 2017-05-12 Mai Alzamel , Panagiotis Charalampopoulos , Costas S. Iliopoulos , Solon P. Pissis , Jakub Radoszewski , Wing-Kin Sung

Assume that an $N$-bit sequence $S$ of $k$ numbers encoded as Elias gamma codes is given as input. We present space-efficient algorithms for sorting, dense ranking and competitive ranking on $S$ in the word RAM model with word size…

Data Structures and Algorithms · Computer Science 2024-09-04 Frank Kammer , Johannes Meintrup , Andrej Sajenko

We examine sorting algorithms for $n$ elements whose basic operation is comparing $t$ elements simultaneously (a $t$-comparator). We focus on algorithms that use only a single round or two rounds -- comparisons performed in the second round…

Data Structures and Algorithms · Computer Science 2024-05-22 Ran Gelles , Zvi Lotker , Frederik Mallmann-Trenn

The integer complexity $f(n)$ of a positive integer $n$ is defined as the minimum number of 1's needed to represent $n$, using additions, multiplications and parentheses. We present two simple and faster algorithms for computing the integer…

Data Structures and Algorithms · Computer Science 2023-09-14 Qizheng He

We consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering \topk{} queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be…

Data Structures and Algorithms · Computer Science 2021-07-13 Seungbum Jo , Srinivasa Rao Satti

In the fillable array problem one must maintain an array A[1..n] of $w$-bit entries subject to random access reads and writes, and also a $\texttt{fill}(\Delta)$ operation which sets every entry of to some $\Delta\in\{0,\ldots,2^w-1\}$. We…

Data Structures and Algorithms · Computer Science 2017-09-28 Jacob Teo Por Loong , Jelani Nelson , Huacheng Yu

We empirically study sorting in the evolving data model. In this model, a sorting algorithm maintains an approximation to the sorted order of a list of data items while simultaneously, with each comparison made by the algorithm, an…

Data Structures and Algorithms · Computer Science 2018-05-16 Juan Jose Besa , William E. Devanny , David Eppstein , Michael Goodrich , Timothy Johnson

In this paper we give an algorithm for computing the mth base-b digit (m=1 is the least significant digit) of an integer n (actually, it finds sharp approximations to n/b^m mod 1), where n is defined as the last number in a sequence of…

Number Theory · Mathematics 2007-05-23 Ernie Croot

Many emerging computer applications require the processing of large numbers, larger than what a CPU can handle. In fact, the top of the line PCs can only manipulate numbers not longer than 32 bits or 64 bits. This is due to the size of the…

Data Structures and Algorithms · Computer Science 2012-04-03 Youssef Bassil , Aziz Barbar

We introduce a sorting machine consisting of $k+1$ stacks in series: the first $k$ stacks can only contain elements in decreasing order from top to bottom, while the last one has the opposite restriction. This device generalizes \cite{SM},…

Data Structures and Algorithms · Computer Science 2019-10-10 Giulio Cerbai , Lapo Cioni , Luca Ferrari

In this paper we revisit the classical regular expression matching problem, namely, given a regular expression $R$ and a string $Q$, decide if $Q$ matches one of the strings specified by $R$. Let $m$ and $n$ be the length of $R$ and $Q$,…

Data Structures and Algorithms · Computer Science 2007-05-23 Philip Bille

Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…

Data Structures and Algorithms · Computer Science 2019-08-14 Benjamin Aram Berendsohn , László Kozma , Dániel Marx

We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…

Combinatorics · Mathematics 2018-08-14 Toufik Mansour , Howard Skogman , Rebecca Smith

We study self-improving sorting with hidden partitions. Our result is an optimal algorithm which runs in expected time O(H(\pi(I)) + n), where I is the given input which contains n elements to be sorted, \pi(I) is the output which are the…

Computational Geometry · Computer Science 2019-02-04 Siu-Wing Cheng , Man-Kwun Chiu , Kai Jin

Consistent hashing is a technique that can minimize key remapping when the number of hash buckets changes. The paper proposes a fast consistent hash algorithm (called power consistent hash) that has $O(1)$ expected time for key lookup,…

Data Structures and Algorithms · Computer Science 2023-12-29 Eric Leu

In this paper we are interested in indexing texts for substring matching queries with one edit error. That is, given a text $T$ of $n$ characters over an alphabet of size $\sigma$, we are asked to build a data structure that answers the…

Data Structures and Algorithms · Computer Science 2014-08-25 Djamal Belazzougui

We consider the problem of preprocessing a text $T$ of length $n$ and a dictionary $\mathcal{D}$ in order to be able to efficiently answer queries $CountDistinct(i,j)$, that is, given $i$ and $j$ return the number of patterns from…

Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…

Machine Learning · Computer Science 2021-07-15 Felix Petersen , Christian Borgelt , Hilde Kuehne , Oliver Deussen