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Unit 42

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
Uniform Generation of Temporal Graphs with Given Degrees
Daniel Allendorf · 2023-04-19 · via cs.DS updates on arXiv.org

Uniform sampling from the set $\mathcal{G}(\mathbf{d})$ of graphs with a given degree-sequence $\mathbf{d} = (d_1, \dots, d_n) \in \mathbb N^n$ is a classical problem in the study of random graphs. We consider an analogue for temporal graphs in which the edges are labeled with integer timestamps. The input to this generation problem is a tuple $\mathbf{D} = (\mathbf{d}, T) \in \mathbb N^n \times \mathbb N_{>0}$ and the task is to output a uniform random sample from the set $\mathcal{G}(\mathbf{D})$ of temporal graphs with degree-sequence $\mathbf{d}$ and timestamps in the interval $[1, T]$. By allowing repeated edges with distinct timestamps, $\mathcal{G}(\mathbf{D})$ can be non-empty even if $\mathcal{G}(\mathbf{d})$ is, and as a consequence, existing algorithms are difficult to apply. We describe an algorithm for this generation problem which runs in expected time $O(M)$ if $Δ^{2+ε} = O(M)$ for some constant $ε> 0$ and $T - Δ= Ω(T)$ where $M = \sum_i d_i$ and $Δ= \max_i d_i$. Our algorithm applies the switching method of McKay and Wormald $[1]$ to temporal graphs: we first generate a random temporal multigraph and then remove self-loops and duplicated edges with switching operations which rewire the edges in a degree-preserving manner.