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

人人都是产品经理
人人都是产品经理
Stack Overflow Blog
Stack Overflow Blog
L
LINUX DO - 最新话题
Google Online Security Blog
Google Online Security Blog
Schneier on Security
Schneier on Security
Spread Privacy
Spread Privacy
www.infosecurity-magazine.com
www.infosecurity-magazine.com
雷峰网
雷峰网
Google DeepMind News
Google DeepMind News
Microsoft Azure Blog
Microsoft Azure Blog
IT之家
IT之家
V
Vulnerabilities – Threatpost
K
Kaspersky official blog
S
Schneier on Security
B
Blog
The Register - Security
The Register - Security
SecWiki News
SecWiki News
Hacker News: Ask HN
Hacker News: Ask HN
cs.AI updates on arXiv.org
cs.AI updates on arXiv.org
S
Security Affairs
T
The Blog of Author Tim Ferriss
G
Google Developers Blog
T
Tenable Blog
P
Proofpoint News Feed
Apple Machine Learning Research
Apple Machine Learning Research
D
DataBreaches.Net
S
Secure Thoughts
Security Latest
Security Latest
H
Heimdal Security Blog
The Hacker News
The Hacker News
O
OpenAI News
AWS News Blog
AWS News Blog
量子位
Exploit-DB.com RSS Feed
Exploit-DB.com RSS Feed
腾讯CDC
U
Unit 42
L
Lohrmann on Cybersecurity
cs.CL updates on arXiv.org
cs.CL updates on arXiv.org
L
LangChain Blog
阮一峰的网络日志
阮一峰的网络日志
T
The Exploit Database - CXSecurity.com
NISL@THU
NISL@THU
cs.CV updates on arXiv.org
cs.CV updates on arXiv.org
Application and Cybersecurity Blog
Application and Cybersecurity Blog
Hugging Face - Blog
Hugging Face - Blog
The Last Watchdog
The Last Watchdog
Recorded Future
Recorded Future
V2EX - 技术
V2EX - 技术
爱范儿
爱范儿
F
Full Disclosure

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 Adaptive Multi-Round Allocation with Stochastic Arrivals The tractability landscape of diffusion alignment: regularization, rewards, and computational primitives Mistake-Bounded Language Generation Positional LSH: Binary Block Matrix Approximation for Attention with Linear Biases Learning-Augmented Scalable Linear Assignment Problem Optimization via Neural Dual Warm-Starts A Note on Non-Negative $L_1$-Approximating Polynomials Curvature Beyond Positivity: Greedy Guarantees for Arbitrary Submodular Functions Convex Optimization with Nested Evolving Feasible Sets On the Complexity of the Matching Problem of Regular Expressions with Backreferences Simple KNN-Based Outlier Detection Achieves Robust Clustering Online Allocation with Unknown Shared Supply Equivalence of Coarse and Fine-Grained Models for Learning with Distribution Shift Accelerated Relax-and-Round for Concave Coverage Problems Contrastive Identification and Generation in the Limit Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Proven Nearly Optimal Attention Coresets On Computing Total Variation Distance Between Mixtures of Product Distributions Exact and Approximate Algorithms for Polytree Learning Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch New Bounds for Kernel Sums via Fast Spherical Embeddings Unlearning Offline Stochastic Multi-Armed Bandits Matroid Algorithms Under Size-Sensitive Independence Oracles On the Learning Curves of Revenue Maximization Asymptotically Robust Learning-Augmented Algorithms for Preemptive FIFO Buffer Management Flashback: A Reversible Bilateral Run-Peeling Decomposition of Strings Incremental Strongly Connected Components with Predictions Characterizing Admissible Objective Functions for Hierarchical Clustering Well-Conditioned Oblivious Perturbations in Linear Space Mathematical Foundations for Peer-to-Peer Lattice Computation Graph Neural Network-Informed Predictive Flows for Faster Ford-Fulkerson and PAC-Learnability A weighted angle distance on strings Towards Universal Convergence of Backward Error in Linear System Solvers Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means Tight Bounds for Learning Polyhedra with a Margin Efficiency of Proportional Mechanisms in Online Auto-Bidding Advertising Skyline-First Traversal as a Control Mechanism for Multi-Criteria Graph Search Constant-Factor Approximation for the Uniform Decision Tree Limited Perfect Monotonical Surrogates constructed using low-cost recursive linkage discovery with guaranteed output Query Lower Bounds for Diffusion Sampling Early Pruning for Public Transport Routing Adapting Dijkstra for Buffers and Unlimited Transfers Exploiting Low-Rank Structure in Max-K-Cut Problems Partial Optimality in the Preordering Problem High-accuracy log-concave sampling with stochastic queries Learning to Approximate Uniform Facility Location via Graph Neural Networks Linear Regression with Unknown Truncation Beyond Gaussian Features Adaptive Power Iteration Method for Differentially Private PCA Finite and Corruption-Robust Regret Bounds in Online Inverse Linear Optimization under M-Convex Action Sets Learning Mixture Models via Efficient High-dimensional Sparse Fourier Transforms Variance Computation for Weighted Model Counting with Knowledge Compilation Approach Deterministic Coreset for Lp Subspace Online Algorithms for Repeated Optimal Stopping: Balancing Baseline Guarantees and Regret Learned Static Function Data Structures Optimal hypersurface decision trees A Perfectly Truthful Calibration Measure The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithm Best Agent Identification for General Game Playing A Faster Generalized Two-Stage Approximate Top-K Fast and Simple Densest Subgraph with Predictions Smoothed Analysis of Learning from Positive Samples Ineffectiveness for Search and Undecidability of PCSP Meta-Problems Sample-Efficient Optimization over Generative Priors via Coarse Learnability Efficient distributional regression trees learning algorithms for calibrated non-parametric probabilistic forecasts Testing Noise Assumptions of Learning Algorithms Testing Support Size More Efficiently Than Learning Histograms Sharper Bounds for Chebyshev Moment Matching, with Applications Expander Hierarchies for Normalized Cuts on Graphs Multilayer Correlation Clustering Efficient Parameter Estimation of Truncated Boolean Product Distributions Faster Hamiltonian Monte Carlo by Learning Leapfrog Scale: a self-calibrated randomized solution
Large Minors in Expanders
Julia Chuzhoy, Rachit Nimavat · 2019-01-27 · via cs.DS updates on arXiv.org

In this paper we study expander graphs and their minors. Specifically, we attempt to answer the following question: what is the largest function $f(n,α,d)$, such that every $n$-vertex $α$-expander with maximum vertex degree at most $d$ contains {\bf every} graph $H$ with at most $f(n,α,d)$ edges and vertices as a minor? Our main result is that there is some universal constant $c$, such that $f(n,α,d)\geq \frac{n}{c\log n}\cdot \left(\fracα{d}\right )^c$. This bound achieves a tight dependence on $n$: it is well known that there are bounded-degree $n$-vertex expanders, that do not contain any grid with $Ω(n/\log n)$ vertices and edges as a minor. The best previous result showed that $f(n,α,d) \geq Ω(n/\log^κn)$, where $κ$ depends on both $α$ and $d$. Additionally, we provide a randomized algorithm, that, given an $n$-vertex $α$-expander with maximum vertex degree at most $d$, and another graph $H$ containing at most $\frac{n}{c\log n}\cdot \left(\fracα{d}\right )^c$ vertices and edges, with high probability finds a model of $H$ in $G$, in time poly$(n)\cdot (d/α)^{O\left( \log(d/α) \right)}$. We note that similar but stronger results were independently obtained by Krivelevich and Nenadov: they show that $f(n,α,d)=Ω\left(\frac{nα^2}{d^2\log n} \right)$, and provide an efficient algorithm, that, given an $n$-vertex $α$-expander of maximum vertex degree at most $d$, and a graph $H$ with $O\left( \frac{nα^2}{d^2\log n} \right)$ vertices and edges, finds a model of $H$ in $G$. Finally, we observe that expanders are the `most minor-rich' family of graphs in the following sense: for every $n$-vertex and $m$-edge graph $G$, there exists a graph $H$ with $O \left( \frac{n+m}{\log n} \right)$ vertices and edges, such that $H$ is not a minor of $G$.