Online analytical processing (OLAP) is a core functionality in database systems. The performance of OLAP is crucial to make online decisions in many applications. However, it is rather costly to support OLAP on large datasets, especially big data, and the methods that compute exact answers cannot meet the high-performance requirement. To alleviate this problem, approximate query processing (AQP) has been proposed, which aims to find an approximate answer as close as to the exact answer efficiently. Existing AQP techniques can be broadly categorized into two categories. (1) Online aggregation: select samples online and use these samples to answer OLAP queries. (2) Offline synopses generation: generate synopses offline based on a-priori knowledge (e.g., data statistics or query workload) and use these synopses to answer OLAP queries. We discuss the research challenges in AQP and summarize existing techniques to address these challenges. In addition, we review how to use AQP to support other complex data types, e.g., spatial data and trajectory data, and support other applications, e.g., data visualization and data cleaning. We also introduce existing AQP systems and summarize their advantages and limitations. Lastly, we provide research challenges and opportunities of AQP. We believe that the survey can help the partitioners to understand existing AQP techniques and select appropriate methods in their applications.
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