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

爱范儿
爱范儿
T
The Blog of Author Tim Ferriss
G
Google Developers Blog
博客园_首页
博客园 - 【当耐特】
量子位
S
SegmentFault 最新的问题
B
Blog RSS Feed
酷 壳 – CoolShell
酷 壳 – CoolShell
V
Visual Studio Blog
T
Tailwind CSS Blog
阮一峰的网络日志
阮一峰的网络日志
V
V2EX
Y
Y Combinator Blog
博客园 - 聂微东
The Cloudflare Blog
小众软件
小众软件
J
Java Code Geeks
freeCodeCamp Programming Tutorials: Python, JavaScript, Git & More
月光博客
月光博客
H
Help Net Security
Jina AI
Jina 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
宝玉的分享
宝玉的分享

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
Directed and Undirected Vertex Connectivity Problems are ...
Olivier Fischer, Yonggang Jiang, Sagnik Mukhopadhyay, Sorrachai · 2025-08-28 · via cs.DS updates on arXiv.org

Vertex connectivity and its variants are among the most fundamental problems in graph theory, with decades of extensive study and numerous algorithmic advances. The directed variants of vertex connectivity are usually solved by manually extending fast algorithms for undirected graphs, which has required considerable effort. In this paper, we present an extremely simple reduction from directed to undirected vertex connectivity for dense graphs. As immediate corollaries, we vastly simplify the proof for directed vertex connectivity in $n^{2+o(1)}$ time [LNPSY25], and obtain a parallel vertex connectivity algorithm for directed graphs with $n^{ω+o(1)}$ work and $n^{o(1)}$ depth, via the undirected vertex connectivity algorithm of [BJMY25]. Our reduction further extends to the weighted, all-pairs and Steiner versions of the problem. By combining our reduction with the recent subcubic-time algorithm for undirected weighted vertex cuts [CT25], we obtain a subcubic-time algorithm for weighted directed vertex connectivity, improving upon a three-decade-old bound [HRG00] for dense graphs. For the all-pairs version, by combining the conditional lower bounds on the all-pairs vertex connectivity problem for directed graphs [AGIKPTUW19], we obtain an alternate proof of the conditional lower bound for the all-pairs vertex connectivity problem on undirected graphs, vastly simplifying the proof by [HLSW23].