平衡分配的力量
IF 0.9
3区 数学
Q2 MATHEMATICS
引用次数: 0
摘要
SIAM 离散数学杂志》，第 38 卷，第 1 期，第 529-565 页，2024 年 3 月。 摘要我们引入了一类新的平衡分配过程，其主要特征是 "填充 "负载不足的箱。打包过程就是一个典型的例子：在每一轮中，我们只取一个仓的样本，如果负载低于平均负载，我们就放置尽可能多的球，直到达到平均负载为止；否则，我们只放置一个球。我们证明，对于本类中的任何一个过程，对于任何数量的球，最大负荷和平均负荷之间的差距都是 [math]w.h.p.[math]。对于打包过程，我们还提供了一个匹配的下限。此外，我们还证明了打包过程的样本效率，即每次样本分配的预期球数严格大于 1。最后，我们还证明了 [math] 关于间隙的上界可以扩展到 Mitzenmacher、Prabhakar 和 Shah 所研究的记忆过程[第 43 届 IEEE 计算机科学基础年度研讨会，加拿大不列颠哥伦比亚省温哥华，2002 年，第 799-808 页]。本文章由计算机程序翻译，如有差异，请以英文原文为准。
The Power of Filling in Balanced Allocations
SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 529-565, March 2024.
Abstract. We introduce a new class of balanced allocation processes which are primarily characterized by “filling” underloaded bins. A prototypical example is the Packing process: At each round we only take one bin sample, and if the load is below the average load, then we place as many balls until the average load is reached; otherwise, we place only one ball. We prove that for any process in this class the gap between the maximum and average load is [math] w.h.p. for any number of balls [math]. For the Packing process, we also provide a matching lower bound. Additionally, we prove that the Packing process is sample efficient in the sense that the expected number of balls allocated per sample is strictly greater than one. Finally, we also demonstrate that the upper bound of [math] on the gap can be extended to the Memory process studied by Mitzenmacher, Prabhakar, and Shah [43rd Annual IEEE Symposium on Foundations of Computer Science, Vancouver, BC, Canada, 2002, pp. 799–808].
Abstract. We introduce a new class of balanced allocation processes which are primarily characterized by “filling” underloaded bins. A prototypical example is the Packing process: At each round we only take one bin sample, and if the load is below the average load, then we place as many balls until the average load is reached; otherwise, we place only one ball. We prove that for any process in this class the gap between the maximum and average load is [math] w.h.p. for any number of balls [math]. For the Packing process, we also provide a matching lower bound. Additionally, we prove that the Packing process is sample efficient in the sense that the expected number of balls allocated per sample is strictly greater than one. Finally, we also demonstrate that the upper bound of [math] on the gap can be extended to the Memory process studied by Mitzenmacher, Prabhakar, and Shah [43rd Annual IEEE Symposium on Foundations of Computer Science, Vancouver, BC, Canada, 2002, pp. 799–808].
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来源期刊
CiteScore
1.90
自引率
0.00%
发文量
124
审稿时长
4-8 weeks
期刊介绍：
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.
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