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

云风的 BLOG
云风的 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
J
Java Code Geeks
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
Engineering at Meta
Engineering at Meta
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
小众软件
小众软件
博客园 - 聂微东
酷 壳 – CoolShell
酷 壳 – CoolShell
月光博客
月光博客
Last Week in AI
Last Week in AI
博客园_首页
I
InfoQ
T
Tailwind CSS Blog
爱范儿
爱范儿
雷峰网
雷峰网
Recent Announcements
Recent Announcements
F
Fortinet All Blogs
B
Blog
WordPress大学
WordPress大学
A
About on SuperTechFans
V
Visual Studio Blog
有赞技术团队
有赞技术团队
P
Proofpoint News Feed

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
A Deterministic Algorithm for the MST Problem in Constant...
Krzysztof Nowicki · 2019-12-10 · via cs.DS updates on arXiv.org

In this paper, we show that the Minimum Spanning Tree problem can be solved \emph{deterministically}, in $\mathcal{O}(1)$ rounds of the $\mathsf{Congested}$ $\mathsf{Clique}$ model. In the $\mathsf{Congested}$ $\mathsf{Clique}$ model, there are $n$ players that perform computation in synchronous rounds. Each round consist of a phase of local computation and a phase of communication, in which each pair of players is allowed to exchange $\mathcal{O}(\log n)$ bit messages. The studies of this model began with the MST problem: in the paper by Lotker et al.[SPAA'03, SICOMP'05] that defines the $\mathsf{Congested}$ $\mathsf{Clique}$ model the authors give a deterministic $\mathcal{O}(\log \log n)$ round algorithm that improved over a trivial $\mathcal{O}(\log n)$ round adaptation of Borůvka's algorithm. There was a sequence of gradual improvements to this result: an $\mathcal{O}(\log \log \log n)$ round algorithm by Hegeman et al. [PODC'15], an $\mathcal{O}(\log^* n)$ round algorithm by Ghaffari and Parter, [PODC'16] and an $\mathcal{O}(1)$ round algorithm by Jurdziński and Nowicki, [SODA'18], but all those algorithms were randomized, which left the question about the existence of any deterministic $o(\log \log n)$ round algorithms for the Minimum Spanning Tree problem open. Our result resolves this question and establishes that $\mathcal{O}(1)$ rounds is enough to solve the MST problem in the $\mathsf{Congested}$ $\mathsf{Clique}$ model, even if we are not allowed to use any randomness. Furthermore, the amount of communication needed by the algorithm makes it applicable to some variants of the $\mathsf{MPC}$ model.