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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
Modeling the Small-World Phenomenon with Road Networks
Michael T. Goodrich, Evrim Ozel · 2022-09-21 · via cs.DS updates on arXiv.org

Dating back to two famous experiments by the social-psychologist, Stanley Milgram, in the 1960s, the small-world phenomenon is the idea that all people are connected through a short chain of acquaintances that can be used to route messages. Many subsequent papers have attempted to model this phenomenon, with most concentrating on the "short chain" of acquaintances rather than their ability to efficiently route messages. In this paper, we study the small-world navigability of the U.S. road network, with the goal of providing a model that explains how messages in the original small-world experiments could be routed along short paths using U.S. roads. To this end, we introduce the Neighborhood Preferential Attachment model, which combines elements from Kleinberg's model and the Barabási-Albert model, such that long-range links are chosen according to both the degrees and (road-network) distances of vertices in the network. We empirically evaluate all three models by running a decentralized routing algorithm, where each vertex only has knowledge of its own neighbors, and find that our model outperforms both of these models in terms of the average hop length. Moreover, our experiments indicate that similar to the Barabási-Albert model, networks generated by our model are scale-free, which could be a more realistic representation of acquaintanceship links in the original small-world experiment.