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

IT之家
IT之家
Y
Y Combinator Blog
月光博客
月光博客
Blog — PlanetScale
Blog — PlanetScale
GbyAI
GbyAI
Cyber Security Advisories - MS-ISAC
Cyber Security Advisories - MS-ISAC
博客园 - 三生石上(FineUI控件)
S
SegmentFault 最新的问题
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
美团技术团队
雷峰网
雷峰网
酷 壳 – CoolShell
酷 壳 – CoolShell
Last Week in AI
Last Week in AI
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
有赞技术团队
有赞技术团队
博客园 - 司徒正美
V
Visual Studio Blog
小众软件
小众软件
OSCHINA 社区最新新闻
OSCHINA 社区最新新闻
T
Tailwind CSS Blog
Apple Machine Learning Research
Apple Machine Learning Research
奇客Solidot–传递最新科技情报
奇客Solidot–传递最新科技情报
A
About on SuperTechFans
The Cloudflare Blog

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
Optimal Multi-Pass Lower Bounds for MST in Dynamic Streams
Sepehr Assadi, Gillat Kol, Zhijun Zhang · 2023-12-08 · via cs.DS updates on arXiv.org

The seminal work of Ahn, Guha, and McGregor in 2012 introduced the graph sketching technique and used it to present the first streaming algorithms for various graph problems over dynamic streams with both insertions and deletions of edges. This includes algorithms for cut sparsification, spanners, matchings, and minimum spanning trees (MSTs). These results have since been improved or generalized in various directions, leading to a vastly rich host of efficient algorithms for processing dynamic graph streams. A curious omission from the list of improvements has been the MST problem. The best algorithm for this problem remains the original AGM algorithm that for every integer $p \geq 1$, uses $n^{1+O(1/p)}$ space in $p$ passes on $n$-vertex graphs, and thus achieves the desired semi-streaming space of $\tilde{O}(n)$ at a relatively high cost of $O(\frac{\log{n}}{\log\log{n}})$ passes. On the other hand, no lower bounds beyond a folklore one-pass lower bound is known for this problem. We provide a simple explanation for this lack of improvements: The AGM algorithm for MSTs is optimal for the entire range of its number of passes! We prove that even for the simplest decision version of the problem -- deciding whether the weight of MSTs is at least a given threshold or not -- any $p$-pass dynamic streaming algorithm requires $n^{1+Ω(1/p)}$ space. This implies that semi-streaming algorithms do need $Ω(\frac{\log{n}}{\log\log{n}})$ passes. Our result relies on proving new multi-round communication complexity lower bounds for a variant of the universal relation problem that has been instrumental in proving prior lower bounds for single-pass dynamic streaming algorithms. The proof also involves proving new composition theorems in communication complexity, including majority lemmas and multi-party XOR lemmas, via information complexity approaches.