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Graph pattern cardinality estimation is the problem of estimating the numberof embeddings of a query graph in a data graph. This fundamental problemarises, 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 captureinformation of graphs well. However, these methods suffer from large errors dueto loss of information during summarization and inherent assumptions.Sampling-based methods are unbiased but suffer from large estimation variancedue to large sample space.  To address these limitations, we propose Alley, a hybrid method that combinesboth sampling and synopses. Alley employs 1) a novel sampling strategy, randomwalk with intersection, which effectively reduces the sample space, 2)branching to further reduce variance, and 3) a novel mining approach thatextracts and indexes tangled patterns as synopses which are inherentlydifficult to estimate by sampling. By using them in the online estimationphase, we can effectively reduce the sample space while still ensuringunbiasedness. We establish that Alley has worst-case optimal runtime andapproximation quality guarantees for any given error bound $\epsilon$ andrequired confidence $\mu$. In addition to the theoretical aspect of Alley, ourextensive experiments show that Alley outperforms the state-of-the-art methodsby up to orders of magnitude higher accuracy with similar efficiency.

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