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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
PMV: Pre-partitioned Generalized Matrix-Vector Multiplica...
Chiwan Park, Ha-Myung Park, Minji Yoon, U Kang · 2017-09-26 · via cs.DS updates on arXiv.org

How can we analyze enormous networks including the Web and social networks which have hundreds of billions of nodes and edges? Network analyses have been conducted by various graph mining methods including shortest path computation, PageRank, connected component computation, random walk with restart, etc. These graph mining methods can be expressed as generalized matrix-vector multiplication which consists of few operations inspired by typical matrix-vector multiplication. Recently, several graph processing systems based on matrix-vector multiplication or their own primitives have been proposed to deal with large graphs; however, they all have failed on Web-scale graphs due to insufficient memory space or the lack of consideration for I/O costs. In this paper, we propose PMV (Pre-partitioned generalized Matrix-Vector multiplication), a scalable distributed graph mining method based on generalized matrix-vector multiplication on distributed systems. PMV significantly decreases the communication cost, which is the main bottleneck of distributed systems, by partitioning the input graph in advance and judiciously applying execution strategies based on the density of the pre-partitioned sub-matrices. Experiments show that PMV succeeds in processing up to 16x larger graphs than existing distributed memory-based graph mining methods, and requires 9x less time than previous disk-based graph mining methods by reducing I/O costs significantly.