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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
Graph Iso/Auto-morphism: A Divide-&-Conquer Approach
Can Lu, Jeffrey Xu Yu, Zhiwei Zhang, Hong Cheng · 2019-11-15 · via cs.DS updates on arXiv.org

The graph isomorphism is to determine whether two graphs are isomorphic. A closely related problem is automorphism detection, where an isomorphism between two graphs is a bijection between their vertex sets that preserves adjacency, and an automorphism is an isomorphism from a graph to itself. Applications of graph isomorphism/automorphism include database indexing, network simplification, network anonymization. By graph automorphism, we deal with symmetric subgraph matching (SSM), which is to find all subgraphs that are symmetric to a given subgraph in G. An application of SSM is to identify multiple seed sets that have the same influence power as a seed set found by influence maximization in a social network. To test two graphs for isomorphism, canonical labeling has been studied to relabel a graph in such a way that isomorphic graphs are identical after relabeling. Efficient canonical labeling algorithms have been designed by individualization-refinement. They enumerate all permutations using a search tree, and select the minimum as the canonical labeling, which prunes candidates during enumeration. Despite high performance in benchmark graphs, these algorithms face difficulties in handling massive graphs. In this paper, we design a new efficient canonical labeling algorithm DviCL. Different from previous algorithms, we take a divide-&-conquer approach to partition G. By partitioning G, an AutoTree is constructed, which preserves symmetric structures and the automorphism group of G. The canonical labeling for a tree node can be obtained by the canonical labeling of its child nodes, and the canonical labeling for the root is the one for G. Such AutoTree can also be effectively used to answer the automorphism group, symmetric subgraphs. We conducted extensive performance studies using 22 large graphs, and confirmed that DviCL is much more efficient and robust than the state-of-the-art.