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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
$k$ disjoint $st$-paths activation in polynomial time
Zeev Nutov · 2021-11-07 · via cs.DS updates on arXiv.org

In activation network design problems we are given an undirected graph $G=(V,E)$ and a pair of activation costs $\{c_e^u,c_e^v\}$ for each $e=uv \in E$. The goal is to find an edge set $F \subseteq E$ that satisfies a prescribed property of minimum activation cost $τ(F)=\sum_{v \in V} \max \{c_e^v: e \in F \mbox{ is incident to } v\}$. In the Activation $k$ Disjoint Paths problem we are given $s,t \in V$ and an integer $k$, and seek an edge set $F \subseteq E$ of $k$ internally disjoint $st$-paths of minimum activation cost. The problem admits an easy $2$-approximation algorithm. However, it was an open question whether the problem is in P even for $k=2$ and power activation costs, when $c_e^u=c_e^v$ for all $e=uv \in E$. Here we will answer this question by giving a polynomial time algorithm using linear programing. We will also mention several consequences, among them a polynomial time algorithm for the Activation 2 Edge Disjoint Paths problem, and improved approximation ratios for the Min-Power $k$-Connected Subgraph problem.