| The intermediate result cardinality { t h e n umber of objects satisfying a condition given in a query { is an important factor for estimating the cost of the query in query optimization. In this paper we s h o w that an object-oriented query often involves partial participation of classes in a relationship. We then present a n e w t e c hnique for estimating the intermediate result cardinality i n such a query. Partial participation has not been considered seriously in existing techniques. Since the proposed technique uses detailed statistics to accommodate partial participation, it estimates the intermediate result cardinality more accurately than existing ones. We also show that these statistics are easily obtained by using inherent properties of object-oriented databases.

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Ray tracing requires many ray-obect intersection tests. A way of reducing the number of ray-object intersection tests is to subdivide the space occupied by objects into many nonoverlapping subregions, called voxels, and to construct an octree for the subdivided space. In this paper, we propose the Octree-R, an octree-variant data structure for efficient ray tracing. The algorithm for constructing the Octree-R first estimates the number of ray-object intersection tests. Then, it partitions the space along the plane that minimizes the estimated number of rayobject intersection tests. We present the results of experiments for verifying the effectiveness of the Octree-R. In the experiment, the Octree-R provides a 4% to 47% performance gain over the conventional octree. The result shows the more skewed the object distribution (as is typical for real data), the more performance gain the Octree-R achieves.Index Terms-Ray tracing octree, Octree-R, space subdivision.

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