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
Blog — PlanetScale
Blog — PlanetScale
博客园 - 【当耐特】
博客园_首页
The GitHub Blog
The GitHub Blog
月光博客
月光博客
Hugging Face - Blog
Hugging Face - Blog
有赞技术团队
有赞技术团队
博客园 - 三生石上(FineUI控件)
D
Docker
Stack Overflow Blog
Stack Overflow Blog
WordPress大学
WordPress大学
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
Apple Machine Learning Research
Apple Machine Learning Research
Vercel News
Vercel News
酷 壳 – CoolShell
酷 壳 – CoolShell
雷峰网
雷峰网
小众软件
小众软件
I
InfoQ
A
About on SuperTechFans
T
The Blog of Author Tim Ferriss
S
SegmentFault 最新的问题
Microsoft Azure Blog
Microsoft Azure Blog
博客园 - Franky

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
Color Fault-Tolerant Distance Preservers: Õptimal Size in...
Merav Parter, Asaf Petruschka · 2025-04-25 · via cs.DS updates on arXiv.org

We revisit the problem of fault-tolerant (FT) distance preservers, when failure events in the network admit a form of correlation modeled as color faults. FT distance preservers are sparse subgraphs that preserve distances between specified pairs of vertices, even after some edge or vertex failures occur. In the classical fault model, any set of at most $k$ edges or vertices might fail (where $k \geq 1$ is a given parameter). Despite extensive research, the classical model admits significant and tantalizing gaps, both in terms of sparsity bounds and of algorithmic efficiency. In this work, we study the problem in the recently introduced color fault-tolerant (CFT) model: the given graph $G=(V,E)$ has arbitrary colors on its edges/vertices where each color appears at most $k$ times, and is susceptible to color faults, where the failure of color $c$ causes all the $c$-colored elements to crash. Our main contribution is in the multi-source setting, where $G$ has a source-set $S \subseteq V$, and the CFT preserver should preserve $S \times V$ distances under any single color fault. We show the following results (where $n = |V|$, $m = |E|$): - There exists a CFT distance preserver $H$ of $G$ with $\tilde{O}(n^{2 - \frac{1}{k+1}} \cdot |S|^{\frac{1}{k+1}} )$ edges. - The above sparsity bound is worst-case optimal up to polylogarithmic terms. - There is a combinatorial randomized algorithm that produces a preserver $H$ whose size meets the above optimal sparsity bound, with running time of $\tilde{O}(m \cdot n^{1 - \frac{1}{k+1}} \cdot |S|^{\frac{1}{k+1}})$. - The above running time is conditionally optimal: a polynomial improvement would refute the combinatorial Boolean Matrix Multiplication (BMM) conjecture. Furthermore, the running time remains optimal even if we only require mild sparsification to $m^{1-ε}$ edges.