{"title":"Discrepancy Minimization via a Self-Balancing Walk","authors":"Ryan Alweiss, Yang P. Liu, Mehtaab S. Sawhney","doi":"10.1137/21m1442450","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Computing, Ahead of Print. <br/> Abstract. We study discrepancy minimization for vectors in [math] under various settings. The main result is the analysis of a new simple random process in high dimensions through a comparison argument. As corollaries, we obtain bounds which are tight up to logarithmic factors for online vector balancing against oblivious adversaries, resolving several questions posed by Bansal et al. [STOC, ACM, New York, 2020, pp. 1139–1152], as well as a linear time algorithm for logarithmic bounds for the Komlós conjecture.","PeriodicalId":49532,"journal":{"name":"SIAM Journal on Computing","volume":"123 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1137/21m1442450","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Computing, Ahead of Print. Abstract. We study discrepancy minimization for vectors in [math] under various settings. The main result is the analysis of a new simple random process in high dimensions through a comparison argument. As corollaries, we obtain bounds which are tight up to logarithmic factors for online vector balancing against oblivious adversaries, resolving several questions posed by Bansal et al. [STOC, ACM, New York, 2020, pp. 1139–1152], as well as a linear time algorithm for logarithmic bounds for the Komlós conjecture.
SIAM 计算期刊》，提前印刷。 摘要我们研究了[math]中各种设置下向量的差异最小化。主要结果是通过比较论证分析了一种新的高维简单随机过程。作为推论，我们得到了针对遗忘对手的在线矢量平衡的对数紧约束，解决了 Bansal 等人提出的几个问题[STOC, ACM, New York, 2020, pp.
期刊介绍：
The SIAM Journal on Computing aims to provide coverage of the most significant work going on in the mathematical and formal aspects of computer science and nonnumerical computing. Submissions must be clearly written and make a significant technical contribution. Topics include but are not limited to analysis and design of algorithms, algorithmic game theory, data structures, computational complexity, computational algebra, computational aspects of combinatorics and graph theory, computational biology, computational geometry, computational robotics, the mathematical aspects of programming languages, artificial intelligence, computational learning, databases, information retrieval, cryptography, networks, distributed computing, parallel algorithms, and computer architecture.
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