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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
Disaster Management in Scale-Free Networks: Recovery from...
Behnam A. Rezaei, Nima Sarshar, P. Oscar Boykin, Vwani P. Roycho · 2005-04-08 · via cs.DS updates on arXiv.org

Susceptibility of scale free Power Law (PL) networks to attacks has been traditionally studied in the context of what may be termed as {\em instantaneous attacks}, where a randomly selected set of nodes and edges are deleted while the network is kept {\em static}. In this paper, we shift the focus to the study of {\em progressive} and instantaneous attacks on {\em reactive} grown and random PL networks, which can respond to attacks and take remedial steps. In the process, we present several techniques that managed networks can adopt to minimize the damages during attacks, and also to efficiently recover from the aftermath of successful attacks. For example, we present (i) compensatory dynamics that minimize the damages inflicted by targeted progressive attacks, such as linear-preferential deletions of nodes in grown PL networks; the resulting dynamic naturally leads to the emergence of networks with PL degree distributions with exponential cutoffs; (ii) distributed healing algorithms that can scale the maximum degree of nodes in a PL network using only local decisions, and (iii) efficient means of creating giant connected components in a PL network that has been fragmented by attacks on a large number of high-degree nodes. Such targeted attacks are considered to be a major vulnerability of PL networks; however, our results show that the introduction of only a small number of random edges, through a {\em reverse percolation} process, can restore connectivity, which in turn allows restoration of other topological properties of the original network. Thus, the scale-free nature of the networks can itself be effectively utilized for protection and recovery purposes.