Efficient and Near-optimal Algorithms for Sampling Small Connected Subgraphs

Efficient and Near-optimal Algorithms for Sampling Small Connected Subgraphs

We study the following problem: Given an integer k ≥ 3 and a simple graph G, sample a connected induced k-vertex subgraph of G uniformly at random. This is a fundamental graph mining primitive with applications in social network analysis, bioinformatics, and more. Surprisingly, no efficient algorith...

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Veröffentlicht in:ACM transactions on algorithms 2023-06, Vol.19 (3), p.1-40, Article 26
1. Verfasser: Bressan, Marco
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Graph algorithms
Mathematics of computing
Random walks and Markov chains
Streaming, sublinear and near linear time algorithms
Theory of computation
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description We study the following problem: Given an integer k ≥ 3 and a simple graph G, sample a connected induced k-vertex subgraph of G uniformly at random. This is a fundamental graph mining primitive with applications in social network analysis, bioinformatics, and more. Surprisingly, no efficient algorithm is known for uniform sampling; the only somewhat efficient algorithms available yield samples that are only approximately uniform, with running times that are unclear or suboptimal. 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.
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subjects Graph algorithms
Mathematics of computing
Random walks and Markov chains
Streaming, sublinear and near linear time algorithms
Theory of computation
title Efficient and Near-optimal Algorithms for Sampling Small Connected Subgraphs
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