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Related papers: Algorithms for Carmichael numbers

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Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…

Information Theory · Computer Science 2017-10-26 Jingge Zhu , Ye Pu , Vipul Gupta , Claire Tomlin , Kannan Ramchandran

We prove that for each odd number k, the sequence (k2^n+1)_{n\ge 1} contains only a finite number of Carmichael numbers. We also prove that k=27 is the smallest value for which such a sequence contains some Carmichael number.

Number Theory · Mathematics 2013-05-16 Javer Cilleruelo , Florian Luca , Amalia Pizarro

We lay the foundations of a new theory for algorithms and computational complexity by parameterizing the instances of a computational problem as a moduli scheme. Considering the geometry of the scheme associated to 3-SAT, we separate P and…

Computational Complexity · Computer Science 2024-02-20 Ali Çivril

The primary Carmichael numbers were recently introduced as a special subset of the Carmichael numbers. A primary Carmichael number $m$ has the unique property that $s_p(m) = p$ holds for each prime factor $p$, where $s_p(m)$ is the sum of…

Number Theory · Mathematics 2024-06-25 Bernd C. Kellner

Submodular maximization subject to matroid constraints is a central problem with many applications in machine learning. As algorithms are increasingly used in decision-making over datapoints with sensitive attributes such as gender or race,…

Data Structures and Algorithms · Computer Science 2026-01-16 Sepideh Mahabadi , Sherry Sarkar , Jakub Tarnawski

We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…

Quantum Physics · Physics 2007-05-23 Harry Buhrman , Ronald de Wolf

Motivated by Internet targeted advertising, we address several ad allocation problems. Prior work has established these problems admit no randomized online algorithm better than $(1-\frac{1}{e})$-competitive…

Data Structures and Algorithms · Computer Science 2015-04-30 Joseph , Naor , David Wajc

We consider the classical online scheduling problem P||C_{max} in which jobs are released over list and provide a nearly optimal online algorithm. More precisely, an online algorithm whose competitive ratio is at most (1+\epsilon) times…

Data Structures and Algorithms · Computer Science 2013-02-19 Lin Chen , Deshi Ye , Guochuan Zhang

Motivated by the problem of enumerating all tree decompositions of a graph, we consider in this article the problem of listing all the minimal chordal completions of a graph. In \cite{carmeli2020} (\textsc{Pods 2017}) Carmeli \emph{et al.}…

Data Structures and Algorithms · Computer Science 2021-07-14 Caroline Brosse , Vincent Limouzy , Arnaud Mary

The problem of fast items retrieval from a fixed collection is often encountered in most computer science areas, from operating system components to databases and user interfaces. We present an approach based on hash tables that focuses on…

Neural and Evolutionary Computing · Computer Science 2020-07-17 Dan Domnita , Ciprian Oprisa

Consider a database most of whose entries are marked but the precise fraction of marked entries is not known. What is known is that the fraction of marked entries is 1-X, where X is a random variable that is uniformly distributed in the…

Quantum Physics · Physics 2007-05-23 Lov K. Grover

In this paper, we initiate a systematic investigation of differentially private algorithms for convex empirical risk minimization. Various instantiations of this problem have been studied before. We provide new algorithms and matching lower…

Machine Learning · Computer Science 2014-10-21 Raef Bassily , Adam Smith , Abhradeep Thakurta

We present the first linear time complexity randomized algorithms for unbiased approximation of the celebrated family of general random walk kernels (RWKs) for sparse graphs. This includes both labelled and unlabelled instances. The…

Machine Learning · Computer Science 2024-10-16 Krzysztof Choromanski , Isaac Reid , Arijit Sehanobish , Avinava Dubey

We study an interval ordering problem introduced by D\"urr et al. [Discrete Appl. Math. 2012] which is motivated by applications in bioinformatics. The task is to order a given set of n intervals with the goal of minimizing a certain…

Data Structures and Algorithms · Computer Science 2026-05-08 Simeon Pawlowski , Vincent Froese

We present a unified framework for minimizing average completion time for many seemingly disparate online scheduling problems, such as the traveling repairperson problems (TRP), dial-a-ride problems (DARP), and scheduling on unrelated…

Data Structures and Algorithms · Computer Science 2021-05-18 Marcin Bienkowski , Artur Kraska , Hsiang-Hsuan Liu

In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…

Statistics Theory · Mathematics 2025-06-17 Bertrand Even , Christophe Giraud , Nicolas Verzelen

We study the hardness of Approximate Query Processing (AQP) of various types of queries involving joins over multiple tables of possibly different sizes. In the case where the query result is a single value (e.g., COUNT, SUM, and…

Databases · Computer Science 2020-10-02 Tianyu Liu , Chi Wang

In this paper we present the experimental results that more clearly than any theory suggest an answer to the question: when in detection of large (probably) prime numbers to apply, a very resource demanding, Miller-Rabin algorithm. Or, to…

Cryptography and Security · Computer Science 2014-01-10 Dragan Vidakovic , Dusko Parezanovic , Zoran Vucetic

We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm,…

Machine Learning · Statistics 2025-02-25 Raymond Zhang , Hedi Hadiji , Richard Combes

Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-10-05 François Le Gall