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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
Xheal: Localized Self-healing using Expanders
Gopal Pandurangan, Amitabh Trehan · 2011-04-06 · via cs.DS updates on arXiv.org

We consider the problem of self-healing in reconfigurable networks (e.g. peer-to-peer and wireless mesh networks) that are under repeated attack by an omniscient adversary and propose a fully distributed algorithm, Xheal that maintains good expansion and spectral properties of the network, also keeping the network connected. Moreover, Xheal does this while allowing only low stretch and degree increase per node. Thus, the algorithm heals global properties while only doing local changes and using only local information. Our work improves over the self-healing algorithms 'Forgiving tree'[PODC 2008] and 'Forgiving graph'[PODC 2009] (using a similar model) in that we are able to give guarantees on degree and stretch, while at the same time preserving the expansion and spectral properties of the network. These repairs preserve the invariants in the following sense. At any point in the algorithm, the expansion of the graph will be either `better' than the expansion of the graph formed by considering only the adversarial insertions (not the adversarial deletions) or the expansion will be, at least, a constant. Also, the stretch i.e. the distance between any pair of nodes in the healed graph is no more than a $O(\log n)$ factor. Similarly, at any point, a node $v$ whose degree would have been $d$ in the graph with adversarial insertions only, will have degree at most $O(κd)$ in the actual graph, for a small parameter $κ$. We also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Our distributed data structure has low amortized latency and bandwidth requirements.