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

Hugging Face - Blog
Hugging Face - Blog
量子位
H
Help Net Security
Microsoft Azure Blog
Microsoft Azure Blog
MongoDB | Blog
MongoDB | Blog
小众软件
小众软件
爱范儿
爱范儿
博客园 - 【当耐特】
Vercel News
Vercel News
S
SegmentFault 最新的问题
M
MIT News - Artificial intelligence
F
Fortinet All Blogs
Apple Machine Learning Research
Apple Machine Learning Research
GbyAI
GbyAI
博客园 - 叶小钗
博客园_首页
V
Visual Studio Blog
宝玉的分享
宝玉的分享
B
Blog
MyScale Blog
MyScale Blog
C
Check Point Blog
博客园 - 三生石上(FineUI控件)
L
LangChain Blog
V
V2EX

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
A simpler QPTAS for scheduling jobs with precedence const...
Syamantak Das, Andreas Wiese · 2025-01-16 · via cs.DS updates on arXiv.org

We study the classical scheduling problem of minimizing the makespan of a set of unit size jobs with precedence constraints on parallel identical machines. Research on the problem dates back to the landmark paper by Graham from 1966 who showed that the simple List Scheduling algorithm is a $(2-\frac{1}{m})$-approximation. Interestingly, it is open whether the problem is NP-hard if $m=3$ which is one of the few remaining open problems in the seminal book by Garey and Johnson. Recently, quite some progress has been made for the setting that $m$ is a constant. In a break-through paper, Levey and Rothvoss presented a $(1+ε)$-approximation with a running time of $n^{(\log n)^{O((m^{2}/ε^{2})\log\log n)}}$[STOC 2016, SICOMP 2019] and this running time was improved to quasi-polynomial by Garg[ICALP 2018] and to even $n^{O_{m,ε}(\log^{3}\log n)}$ by Li[SODA 2021]. These results use techniques like LP-hierarchies, conditioning on certain well-selected jobs, and abstractions like (partial) dyadic systems and virtually valid schedules. In this paper, we present a QPTAS for the problem which is arguably simpler than the previous algorithms. We just guess the positions of certain jobs in the optimal solution, recurse on a set of guessed subintervals, and fill in the remaining jobs with greedy routines. We believe that also our analysis is more accessible, in particular since we do not use (LP-)hierarchies or abstractions of the problem like the ones above, but we guess properties of the optimal solution directly.