Abstract: A method, apparatus, article of manufacture, and data structure for efficiently identifying parent-child relationships of a plurality of members. The parent-child relationships are encoded into a matrix, wherein a particular member is represented by a particular row and a particular column of the matrix. A value at an intersection of a specific one of the rows and a specific one of the columns indicates whether a parent-child relationship exists between the member represented by the row and the member represented by the column. Thereafter, matrix operations may be applied to the matrix.

Abstract: Method and system aspects for efficiently searching an encoded vector index are provided. The aspects include the translation of a search query into a candidate bitmap, and the mapping of data from the candidate bitmap into a search result bitmap according to entry values in the encoded vector index. Further, the translation includes the setting of a bit in the candidate bitmap for each entry in a symbol table that corresponds to candidate of the search query. Also included in the mapping is the identification of a bit value in the candidate bitmap pointed to by an entry in an encoded vector.

Abstract: A method for partitioning keys onto radix tree logical pages and a parallel index page build algorithm in order to provide radix tree build speedup proportional to the number of processors on the system and controlled efficient page utilization. Also, since keys are intelligently partitioned so that a complete set of keys is inserted into a logical page, there is no page overflow during the tree construction and thus page splitting is eliminated. Since radix index trees are really groups of logical pages in which each logical page contains a small tree, the tree is built (with respect to the logical pages) from the bottom up, while within each individual logical page the tree is constructed from the top down. The space required for a logical page is pre-allocated to allow construction of limbs to begin without waiting for the build of their underlying pages to complete.