SPAC: Scalable Pattern Approximate Counting in Graph Mining

Pattern counting is a crucial task in graph pattern mining. Accurate counting is not affordable as the datasets grow larger and larger, and approximate counting is getting popular to provide an estimated answer quickly. However, current approximate counting approaches are still time-consuming and not scalable for extra-large graphs. This paper proposes SPAC, a fast and flexible pattern approximate counting method, based on the observation that pattern number distribution to degrees also follows power-law as the vertices, the common feature in graph datasets. By leveraging the distribution, SPAC can efficiently choose a small number of degrees as samples, fit the coefficients, and then calculate the pattern frequency directly. To provide flexibility for different use-cases, SPAC supports both accurate and approximate counting in the sampling phase. Moreover, edge weighting and interpolation techniques are adopted to emphasize the sample tail to improve fitting accuracy. The prototype of SPAC is implemented with GraphX on Spark, and is evaluated against various well-known graphs. The experimental results show that SPAC is up to 10x faster than accurate counting, keeping the same error level below 10%. Compared to existing approximate counting, SPAC is 1.4x–9x faster in general, while the error could be reduced to 20% of the current systems.