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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
Highway Preferential Attachment Models for Geographic Rou...
2024-03-13 · via cs.DS updates on arXiv.org

In the 1960s, the world-renowned social psychologist Stanley Milgram conducted experiments that showed that not only do there exist ``short chains'' of acquaintances between any two arbitrary people, but that these arbitrary strangers are able to find these short chains. This phenomenon, known as the \emph{small-world phenomenon}, is explained in part by any model that has a low diameter, such as the Barabási and Albert's \emph{preferential attachment} model, but these models do not display the same efficient routing that Milgram's experiments showed. In the year 2000, Kleinberg proposed a model with an efficient $\mathcal{O}(\log^2{n})$ greedy routing algorithm. In 2004, Martel and Nguyen showed that Kleinberg's analysis was tight, while also showing that Kleinberg's model had an expected diameter of only $Θ(\log{n})$ -- a much smaller value than the greedy routing algorithm's path lengths. In 2022, Goodrich and Ozel proposed the \emph{neighborhood preferential attachment} model (NPA), combining elements from Barabási and Albert's model with Kleinberg's model, and experimentally showed that the resulting model outperformed Kleinberg's greedy routing performance on U.S. road networks. While they displayed impressive empirical results, they did not provide any theoretical analysis of their model. In this paper, we first provide a theoretical analysis of a generalization of Kleinberg's original model and show that it can achieve expected $\mathcal{O}(\log{n})$ routing, a much better result than Kleinberg's model. We then propose a new model, \emph{windowed NPA}, that is similar to the neighborhood preferential attachment model but has provable theoretical guarantees w.h.p. We show that this model is able to achieve $\mathcal{O}(\log^{1 + ε}{n})$ greedy routing for any $ε> 0$.