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

T
Tailwind CSS Blog
P
Proofpoint News Feed
V
Visual Studio Blog
H
Hackread – Cybersecurity News, Data Breaches, AI and More
爱范儿
爱范儿
Microsoft Azure Blog
Microsoft Azure Blog
Recent Announcements
Recent Announcements
Vercel News
Vercel News
Hugging Face - Blog
Hugging Face - Blog
GbyAI
GbyAI
博客园 - 聂微东
D
DataBreaches.Net
酷 壳 – CoolShell
酷 壳 – CoolShell
Microsoft Security Blog
Microsoft Security Blog
L
LangChain Blog
美团技术团队
H
Help Net Security
aimingoo的专栏
aimingoo的专栏
C
Check Point Blog
U
Unit 42
博客园 - 叶小钗
有赞技术团队
有赞技术团队
M
MIT News - Artificial intelligence
MongoDB | Blog
MongoDB | 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
Colorful Vertex Recoloring of Bipartite Graphs
Boaz Patt-Shamir, Adi Rosen, Seeun William Umboh · 2025-01-10 · via cs.DS updates on arXiv.org

In vertex recoloring, we are given $n$ vertices with their initial coloring, and edges arrive in an online fashion. The algorithm must maintain a valid coloring by recoloring vertices, at a cost. The problem abstracts a scenario of job placement in machines (possibly in the cloud), where vertices represent jobs, colors represent machines, and edges represent ``anti affinity'' (disengagement) constraints. Online recoloring is a hard problem. One family of instances which is fairly well-understood is bipartite graphs, in which two colors are sufficient to satisfy all constraints. In this case it is known that the competitive ratio of vertex recoloring is $Θ(\log n)$. We propose a generalization of the problem, which allows using additional colors (possibly at a higher cost), to improve overall performance. We analyze the simple case of bipartite graphs of bounded largest \emph{bond} (a bond of a connected graph is an edge-cut that partitions the graph into two connected components). First, we propose two algorithms. One exhibits a trade-off for the uniform-cost case: given $Ω(\logβ)\le c\le O(\log n)$ colors, the algorithm guarantees that its cost is at most $O(\frac{\log n}{c})$ times the optimal offline cost for two colors, where $n$ is the number of vertices and $β$ is the size of the largest bond. The other algorithm is for the case where the additional colors come at a higher cost, $D>1$: given $Δ$ additional colors, where $Δ$ is the maximum degree in the graph, the algorithm guarantees $O(\log D)$ competitiveness. As to lower bounds, we show that if the cost of the extra colors is $D>1$, no (randomized) algorithm can achieve a competitive ratio of $o(\log D)$. We also show that for bipartite graphs of unbounded bond size, any deterministic online algorithm has competitive ratio $Ω(\min(D,\log n))$.