生成二进制万有引力的渐进最优算法

IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Luc Devroye , Dimitrios Los
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引用次数: 0

摘要

在 "球入箱 "设置中,n 个球被均匀随机地扔进 n 个箱中。生成最终载荷向量的简单方法需要花费 Θ(n) 时间。然而,众所周知,这个载荷向量的二进制心数很有可能是 Θ(lognloglogn) 大小。此外,我们提出的算法对于任意 m∈[n,nlogn] 球仍然是最优的,而且还可以用作有效模拟更多负载平衡算法的构件。特别是对于 "二选一 "算法(该算法在每一步中对两个分区进行采样,并分配给其中负载最小的分区),我们获得了比天真模拟大约四倍的速度提升。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An asymptotically optimal algorithm for generating bin cardinalities

In the balls-into-bins setting, n balls are thrown uniformly at random into n bins. The naïve way to generate the final load vector takes Θ(n) time. However, it is well-known that this load vector has with high probability bin cardinalities of size Θ(lognloglogn). Here, we present an algorithm in the RAM model that generates the bin cardinalities of the final load vector in the optimal Θ(lognloglogn) time in expectation and with high probability.

Further, the algorithm that we present is still optimal for any m[n,nlogn] balls and can also be used as a building block to efficiently simulate more involved load balancing algorithms. In particular, for the Two-Choice algorithm, which samples two bins in each step and allocates to the least-loaded of the two, we obtain roughly a quadratic speed-up over the naïve simulation.

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来源期刊
Mathematics and Computers in Simulation
Mathematics and Computers in Simulation 数学-计算机:跨学科应用
CiteScore
8.90
自引率
4.30%
发文量
335
审稿时长
54 days
期刊介绍: The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.
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