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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
Multi-View Structural Graph Summaries
Jonatan Frank, Andor Diera, David Richerby, Ansgar Scherp · 2024-07-25 · via cs.DS updates on arXiv.org

A structural graph summary is a small graph representation that preserves structural information necessary for a given task. The summary is used instead of the original graph to complete the task faster. We introduce multi-view structural graph summaries and propose an algorithm for merging two summaries. We conduct a theoretical analysis of our algorithm. We run experiments on three datasets, contributing two new ones. The datasets are of different domains (web graph, source code, and news) and sizes; the interpretation of multi-view depends on the domain and are pay-level domains on the web, control vs.\@ data flow of the code, and news broadcasters. We experiment with three graph summary models: attribute collection, class collection, and their combination. We observe that merging two structural summaries has an upper bound of quadratic complexity; but under reasonable assumptions, it has linear-time worst-case complexity. The running time of merging has a strong linear correlation with the number of edges in the two summaries. Therefore, the experiments support the assumption that the upper bound of quadratic complexity is not tight and that linear complexity is possible. Furthermore, our experiments show that always merging the two smallest summaries by the number of edges is the most efficient strategy for merging multiple structural summaries.