[Technical Report] Combining Sampling and Synopses with Worst-Case Optimal Runtime and Quality Guarantees for Graph Pattern Cardinality Estimation

Abstract

Graph pattern cardinality estimation is the problem of estimating the number of embeddings of a query graph in a data graph. This fundamental problem arises, for example, during query planning in subgraph matching algorithms. There are two major approaches to solving the problem: sampling and synopsis. Synopsis (or summary)-based methods are fast and accurate if synopses capture information of graphs well. However, these methods suffer from large errors due to loss of information during summarization and inherent assumptions. Sampling-based methods are unbiased but suffer from large estimation variance due to large sample space. To address these limitations, we propose Alley, a hybrid method that combines both sampling and synopses. Alley employs 1) a novel sampling strategy, random walk with intersection, which effectively reduces the sample space, 2) branching to further reduce variance, and 3) a novel mining approach that extracts and indexes tangled patterns as synopses which are inherently difficult to estimate by sampling. By using them in the online estimation phase, we can effectively reduce the sample space while still ensuring unbiasedness. We establish that Alley has worst-case optimal runtime and approximation quality guarantees for any given error bound $\epsilon$ and required confidence $\mu$. In addition to the theoretical aspect of Alley, our extensive experiments show that Alley outperforms the state-of-the-art methods by up to orders of magnitude higher accuracy with similar efficiency.