Related papers: Algorithms for Carmichael numbers
The Ramsey number is of vital importance in Ramsey's theorem. This paper proposed a novel methodology for constructing Ramsey graphs about R(3,10), which uses Artificial Bee Colony optimization(ABC) to raise the lower bound of Ramsey number…
We explore the machine-minimizing job scheduling problem, which has a rich history in the line of research, under an online setting. We consider systems with arbitrary job arrival times, arbitrary job deadlines, and unit job execution time.…
In this paper, we describe an algorithm that efficiently collect relations in class groups of number fields defined by a small defining polynomial. This conditional improvement consists in testing directly the smoothness of principal ideals…
In this paper we analyze the computational costs of various operations and algorithms in algebraic number fields using exact arithmetic. Let $K$ be an algebraic number field. In the first half of the paper, we calculate the running time and…
We consider the weakly supervised binary classification problem where the labels are randomly flipped with probability $1- {\alpha}$. Although there exist numerous algorithms for this problem, it remains theoretically unexplored how the…
Non-monotone constrained submodular maximization plays a crucial role in various machine learning applications. However, existing algorithms often struggle with a trade-off between approximation guarantees and practical efficiency. The…
We show that universal elliptic Carmichael numbers do not exist, answering a question of Silverman. Moreover, we show that the probability that an integer $n$, which is not a prime power, is an elliptic Carmichael number for a random curve…
In the last decade, there has been a substantial amount of research in finding routing algorithms designed specifically to run on real-world graphs. In 2010, Abraham et al. showed upper bounds on the query time in terms of a graph's highway…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
We define a Carmichael number of order m to be a composite integer n such that nth-power raising defines an endomorphism of every Z/nZ-algebra that can be generated as a Z/nZ-module by m elements. We give a simple criterion to determine…
We give an upper bound for the number elliptic Carmichael numbers $n \le x$ that have recently been introduced by J. H. Silverman. We also discuss several possible ways for further improvements.
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations $y = \Phi x$. In many applications, extremely large problem sizes are envisioned, with at least tens of…
This paper addresses the challenging scheduling problem of coflows with release times, with the objective of minimizing the total weighted completion time. Previous literature has predominantly concentrated on establishing the scheduling…
For time-dependent PDEs, the numerical schemes can be rendered bound-preserving without losing conservation and accuracy, by a post processing procedure of solving a constrained minimization in each time step. Such a constrained…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions…