Efficient Complex Aggregate Queries with Accuracy Guarantee Based on Execution Cost Model over Knowledge Graphs

Knowledge graphs (KGs) have gained prominence for representing real-world facts, with queries of KGs being crucial for their application. Aggregate queries, as one of the most important parts of KG queries (e.g., " What is the average price of cars produced in Germany?"), can provide users with valuable statistical insights. An efficient solution for KG aggregate queries is approximate aggregate queries with semantic-aware sampling (AQS). This balances the query time and result accuracy by estimating an approximate aggregate result based on random samples collected from a KG, ensuring that the relative error of the approximate aggregate result is bounded by a predefined error. However, AQS is tailored for simple aggregate queries and exhibits varying performance for complex aggregate queries. This is because a complex aggregate query usually consists of multiple simple aggregate queries, and each sub-query influences the overall processing time and result quality. Setting a large error bound for each sub-query yields quick results but with a lower quality, while aiming for high-quality results demands a smaller predefined error bound for each sub-query, leading to a longer processing time. Hence, devising efficient and effective methods for executing complex aggregate queries has emerged as a significant research challenge within contemporary KG querying. To tackle this challenge, we first introduced an execution cost model tailored for original AQS (i.e., supporting simple queries) and founded on Taylor's theorem. This model aids in identifying the initial parameters that play a pivotal role in the efficiency and efficacy of AQS. Subsequently, we conducted an in-depth exploration of the intrinsic relationship of the error bounds between a complex aggregate query and its constituent simple queries (i.e., sub-queries), and then we formalized an execution cost model for complex aggregate queries, given the accuracy constraints on the error bounds of all sub-queries. Harnessing the multi-objective optimization genetic algorithm, we refined the error bounds of all sub-queries with moderate values, to achieve a balance of query time and result accuracy for the complex aggregate query. An extensive experimental study on real-world datasets demonstrated our solution's superiority in effectiveness and efficiency.