Self-tuning UDF Cost Modeling Using the Memory-Limited Quadtree

Query optimizers in object-relational database management systems require users to provide the execution cost models of user-defined functions(UDFs). Despite this need, however, there has been little work done to provide such a model. Furthermore, none of the existing work is self-tuning and, therefore, cannot adapt to changing UDF execution patterns. This paper addresses this problem by introducing a self-tuning cost modeling approach based on the quadtree. The quadtree has the inherent desirable properties to (1) perform fast retrievals, (2) allow for fast incremental updates (without storing individual data points), and (3) store information at different resolutions. We take advantage of these properties of the quadtree and add the following in order to make the quadtree useful for UDF cost modeling: the abilities to (1) adapt to changing UDF execution patterns and (2) use limited memory. To this end, we have developed a novel technique we call the memory-limited quadtree(MLQ). In MLQ, each instance of UDF execution is mapped to a query point in a multi-dimensional space. Then, a prediction is made at the query point, and the actual value at the point is inserted as a new data point. The quadtree is then used to store summary information of the data points at different resolutions based on the distribution of the data points. This information is used to make predictions, guide the insertion of new data points, and guide the compression of the quadtree when the memory limit is reached. We have conducted extensive performance evaluations comparing MLQ with the existing (static) approach.