While database applications require more complex and sophisticated tasks, common and important database features tend to be implemented within database system. Processing of aggregate operations is crucial in that they are basic operators for analytical processing and have serious impact on system performance. In this thesis, we focus on processing of aggregate operation in database systems. Most commercial products have been supporting these operators. However, their implementations are straightforward and hence degrade system performance in many cases. This is because they deal with only general cases. By exploiting the application specific knowledge, these operations can be processed more efficiently.
In active databases, aggregate operations are usually used in active rules to describe complicated business semantics. In these cases, efficient condition evaluation is crucial for high performance of active database systems. Most previous works used the incremental evaluation techniques, whose operations are relatively expensive due to the processing based on the exact calculation of the condition expression. We propose a new filtering technique that effectively identifies false condition in an early stage of condition monitoring. Since the results of condition evaluation tend to be false in most practical cases, an efficient filtering method can highly facilitate fast condition evaluation. The proposed filtering technique is developed based on the new perspective of database state and database operations, i.e., a vector space model. We first present vector representations of database states, database operations, and complex condition expressions. Then, we propose two filtering methods based on the properties of vector space, called the sphere containment test and the hyperplane test. Our proposed methods determine the truth value of the rule conditions only with the delta vectors maintained in main memory and they can be used at the same time to increase the...