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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 1.5-pproximation algorithms for activating 2 disjoint $...
Zeev Nutov, Dawod Kahba · 2023-07-24 · via cs.DS updates on arXiv.org

In the $Activation$ $k$ $Disjoint$ $st$-$Paths$ ($Activation$ $k$-$DP$) problem we are given a graph $G=(V,E)$ with activation costs $\{c_{uv}^u,c_{uv}^v\}$ for every edge $uv \in E$, a source-sink pair $s,t \in V$, and an integer $k$. The goal is to compute an edge set $F \subseteq E$ of $k$ internally node disjoint $st$-paths of minimum activation cost $\displaystyle \sum_{v \in V}\max_{uv \in E}c_{uv}^v$. The problem admits an easy $2$-approximation algorithm. Alqahtani and Erlebach [CIAC, pages 1-12, 2013] claimed that Activation 2-DP admits a $1.5$-approximation algorithm. Their proof has an error, and we will show that the approximation ratio of their algorithm is at least $2$. We will then give a different algorithm with approximation ratio $1.5$.