惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

Y
Y Combinator Blog
宝玉的分享
宝玉的分享
月光博客
月光博客
小众软件
小众软件
Jina AI
Jina AI
WordPress大学
WordPress大学
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
T
Tailwind CSS Blog
钛媒体:引领未来商业与生活新知
钛媒体:引领未来商业与生活新知
博客园 - 【当耐特】
博客园 - 三生石上(FineUI控件)
博客园 - 司徒正美
大猫的无限游戏
大猫的无限游戏
The Cloudflare Blog
G
Google Developers Blog
M
MIT News - Artificial intelligence
N
Netflix TechBlog - Medium
云风的 BLOG
云风的 BLOG
MyScale Blog
MyScale Blog
让小产品的独立变现更简单 - ezindie.com
让小产品的独立变现更简单 - ezindie.com
爱范儿
爱范儿
U
Unit 42
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
Blog — PlanetScale
Blog — PlanetScale

cs.DS updates on arXiv.org

PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
An Optimal Space Lower Bound for Approximating MAX-CUT
Michael Kapralov, Dmitry Krachun · 2018-11-27 · via cs.DS updates on arXiv.org

We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of edges and output half of this value as the estimate for the size of the MAX-CUT. On the other extreme, for any fixed $ε> 0$, if one allows $\tilde{O}(n)$ space, a $(1+ε)$-approximate solution to the MAX-CUT value can be obtained by storing an $\tilde{O}(n)$-size sparsifier that essentially preserves MAX-CUT value. Our main result is that any (randomized) single pass streaming algorithm that breaks the $2$-approximation barrier requires $Ω(n)$-space, thus resolving the space complexity of any non-trivial approximations of the MAX-CUT value to within polylogarithmic factors in the single pass streaming model. We achieve the result by presenting a tight analysis of the Implicit Hidden Partition Problem introduced by Kapralov et al.[SODA'17] for an arbitrarily large number of players. In this problem a number of players receive random matchings of $Ω(n)$ size together with random bits on the edges, and their task is to determine whether the bits correspond to parities of some hidden bipartition, or are just uniformly random. Unlike all previous Fourier analytic communication lower bounds, our analysis does not directly use bounds on the $\ell_2$ norm of Fourier coefficients of a typical message at any given weight level that follow from hypercontractivity. Instead, we use the fact that graphs received by players are sparse (matchings) to obtain strong upper bounds on the $\ell_1$ norm of the Fourier coefficients of the messages of individual players, and then argue, using the convolution theorem, that similar strong bounds on the $\ell_1$ norm are essentially preserved once messages of different players are combined.