Reinforcement Learning Enhanced Weighted Sampling for Accurate Subgraph Counting on Fully Dynamic Graph Streams

As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and deletions of edges), rendering exact computation of these counts to be infeasible. Common practice is, instead, to use a small set of edges as a sample to estimate the counts. Existing sampling algorithms for fully dynamic graphs sample the edges with uniform probability. In this paper, we show that we can do much better if we sample edges based on their individual properties. Specifically, we propose a weighted sampling algorithm called WSD for estimating the subgraph count in a fully dynamic graph stream, which samples the edges based on their weights that indicate their importance and reflect their properties. We determine the weights of edges in a data-driven fashion, using a novel method based on reinforcement learning. We conduct extensive experiments to verify that our technique can produce estimates with smaller errors while often running faster compared with existing algorithms.

• No Knowledge. We have no knowledge about the stream (e.g., the size of stream, the number of vertices and edges, etc.) in advance.

• Limited Memory. We can store at most M edges in a reservoir, where M is a predefined parameter and independent to the size of the stream.

• Single Pass. Edge insertions and deletions are processed one by one in their arrival order. Edges cannot be accessed again once they are discarded.