In order to better maintain the data integrity and help auditors find anomalous reimbursement records in relational databases, the algorithm AAC-Hunter (Aggregation Algebraic Constraints Hunter), which discovered Aggregation Algebraic Constraints (AACs) automatically, was proposed. An AAC is a fuzzy constraint defined between the aggregation results of two columns in the database and acts on most but not all records. Firstly, joining, grouping and algebraic expressions were enumerated to generate candidate AACs. Secondly, the value range sets of these candidate AACs were calculated. Finally, the AAC results were output. However, this method was not able to face the performance challenges caused by massive data, so that a set of heuristic rules were applied to decrease the size of candidate constraint space and the optimization strategies based on intermediate results reuse and trivial candidate AACs elimination were employed to speed up the value range set calculation for candidate AACs. Experimental results on TPC-H and European Soccer datasets show that AAC-Hunter reduces the constraint discovery space by 95.68% and 99.94% respectively, and shortens running time by 96.58% and 92.51% respectively, compared with the baseline algorithm without heuristic rules or optimization strategies. As the effectiveness of AAC-Hunter is verified, it can be seen that AAC-Hunter can improve the efficiency and capability of auditing application.