文章基本信息
- 标题：Sign Rank vs Discrepancy
- 本地全文：下载
- 作者：Hamed Hatami ; Kaave Hosseini ; Shachar Lovett 等
- 期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
- 电子版ISSN：1868-8969
- 出版年度：2020
- 卷号：169
- 页码：18:1-18:14
- DOI：10.4230/LIPIcs.CCC.2020.18
- 出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
- 摘要：Sign-rank and discrepancy are two central notions in communication complexity. The seminal work of Babai, Frankl, and Simon from 1986 initiated an active line of research that investigates the gap between these two notions. In this article, we establish the strongest possible separation by constructing a boolean matrix whose sign-rank is only 3, and yet its discrepancy is 2^{-Ω(n)}. We note that every matrix of sign-rank 2 has discrepancy n^{-O(1)}. Our result in particular implies that there are boolean functions with O(1) unbounded error randomized communication complexity while having Ω(n) weakly unbounded error randomized communication complexity.
- 关键词：Discrepancy; sign rank; Unbounded-error communication complexity; weakly unbounded error communication complexity
