Metric Sublinear Algorithms Via Linear Sampling Deepai O 1k6 n " log n and expected sampling time per graphlet ko(k)" 10 1 log " theorem 1 (the linear algo). there exists a two phase uniform graphlet sampling algorithm with preprocessing time o(n k2 log k m) o(n m) and expected sampling time per graphlet ko(k) log n o(log n). Explore efficient algorithms for graphlet sampling, including linear and sublinear preprocessing techniques, with applications to semi streaming and mpc settings.
Metric Sublinear Algorithms Via Linear Sampling Deepai We will discuss algorithms for this problem with linear and sublinear preprocessing time, as well as some recent adaptations to the semi streaming and mpc settings. … more. We study the graphlet sampling problem: given an integer $k \ge 3$ and a simple graph $g= (v,e)$, sample a connected induced $k$ node subgraph of $g$ (also called $k$ graphlet) uniformly at random. In this work, we provide: (i) a near optimal mixing time bound for a well known random walk technique, (ii) the first efficient algorithm for truly uniform graphlet sampling, and (iii) the first sublinear time algorithm for ε uniform graphlet sampling. We also show that the tradeoff between memory and number of passes of our algorithms is near optimal. our extensive evaluation on very large graphs shows the effectiveness of our algorithms.
Sublinear Algorithms In this work, we provide: (i) a near optimal mixing time bound for a well known random walk technique, (ii) the first efficient algorithm for truly uniform graphlet sampling, and (iii) the first sublinear time algorithm for ε uniform graphlet sampling. We also show that the tradeoff between memory and number of passes of our algorithms is near optimal. our extensive evaluation on very large graphs shows the effectiveness of our algorithms. In this work, we provide: (i) a near optimal mixing time bound for a well known random walk technique, (ii) the first efficient algorithm for truly uniform graphlet sampling, and (iii) the first sublinear time algorithm for ε uniform graphlet sampling. Input: a simple undirected graph g and k ≥ 3 output: a uniform random connected k vertex subgraph of g (a k graphlet) applications: sampling k graphlets → k graphlet distribution → feature vector graph classification, graph kernels, graph neural networks, clustered federated learning. If either "delta", "epsilon", "a" or "n samples" is given calculates the kernel value for the given (or derived) random picked n samples, by randomly sampling from k from 3 to 5. otherwise calculates the kernel value drawing all possible connected samples of size k. In this work, we propose a general and novel framework to estimate graphlet statistics of any size. our framework is based on collecting samples through consecutive steps of random walk.
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