Efficient Processing of the Cube Operator

This paper presents a part of the doctoral work with the theme: “The impact of sorted reading from UB-trees on relational database systems”. Based on [Mar99] this doctoral work deals with the problems of the efficient implementation and analysis of sorted reading (UB-Cache [Bay97b], Tetris -Algorithm [MB98], [MZB99]) and its effect on query-processing and query optimization in relational databases and especially in the field of data warehousing (DW) and data-mining. In our days, the B-Tree [BM72] is a de facto standard in relational database systems for onedimensional data. Based on the B-Tree a new data structure for multidimensional data, the UB-Tree, was invented by [Bay96]. This data structure utilizes a space-filling curve to partition a multidimensional universe into disjoint regions while preserving multidimensional clustering. A space-filling curve (e.g., Z-curve) maps a ddimensional universe to a one-dimensional universe. Therefore algorithms for point queries, insertion, and multidimensional range queries can be efficiently handled by a normal B*-tree, which is available in any commercial relational database system. In our prototype implementation we use the Z-curve. A Z-address Z(x) is the ordinal number of a tuple x on the Z-curve which is used a key for the B*-Tree [Mar99].