MANIACS: Approximate Mining of Frequent Subgraph Patterns through Sampling

We present MANIACS, a sampling-based randomized algorithm for computing high-quality approximations of the collection of the subgraph patterns that are frequent in a single, large, vertex-labeled graph, according to the Minimum Node Image-based (MNI) frequency measure. The output of MANIACS comes with strong probabilistic guarantees, obtained by using the empirical Vapnik-Chervonenkis (VC) dimension, a key concept from statistical learning theory, together with strong probabilistic tail bounds on the difference between the frequency of a pattern in the sample and its exact frequency. MANIACS leverages properties of the MNI-frequency to aggressively prune the pattern search space, and thus to reduce the time spent in exploring subspaces that contain no frequent patterns. In turn, this pruning leads to better bounds to the maximum frequency estimation error, which leads to increased pruning, resulting in a beneficial feedback effect. The results of our experimental evaluation of MANIACS on real graphs show that it returns high-quality collections of frequent patterns in large graphs up to two orders of magnitude faster than the exact algorithm.