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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
Balancing spreads of influence in a social network
Ruben Becker, Federico Corò, Gianlorenzo D'Angelo, Hugo Gilbert · 2019-06-01 · via cs.DS updates on arXiv.org

The personalization of our news consumption on social media has a tendency to reinforce our pre-existing beliefs instead of balancing our opinions. This finding is a concern for the health of our democracies which rely on an access to information providing diverse viewpoints. To tackle this issue from a computational perspective, Garimella et al. (NIPS'17) modeled the spread of these viewpoints, also called campaigns, using the well-known independent cascade model and studied an optimization problem that aims at balancing information exposure in a social network when two opposing campaigns propagate in the network. The objective in their $NP$-hard optimization problem is to maximize the number of people that are exposed to either both or none of the viewpoints. For two different settings, one corresponding to a model where campaigns spread in a correlated manner, and a second one, where the two campaigns spread in a heterogeneous manner, they provide constant ratio approximation algorithms. In this paper, we investigate a more general formulation of this problem. That is, we assume that $μ$ different campaigns propagate in a social network and we aim to maximize the number of people that are exposed to either $ν$ or none of the campaigns, where $μ\geν\ge2$. We provide dedicated approximation algorithms for both the correlated and heterogeneous settings. Interestingly, for the heterogeneous setting with $ν\ge 3$, we give a reduction leading to several approximation hardness results. Maybe most importantly, we obtain that the problem cannot be approximated within a factor of $n^{-g(n)}$ for any $g(n)=o(1)$ assuming Gap-ETH, denoting with $n$ the number of nodes in the social network. For $ν\ge 4$, there is no $n^{-ε}$-approximation algorithm if a certain class of one-way functions exists, where $ε> 0$ is a given constant which depends on $ν$.