Cube Tree Dimension: number of group-by values Relation tuples map to a point in the space Aggregates: projection of all data points on all the subspaces. Intersection between a subspace and the orthogonal hyper-plane stores the aggregates. Origin represents aggregate with no grouping Query a group-by aggregate on the corresponding hyper-planes

Packed R-Tree Sort-pack: (for multi-dimension data) –Achieves excellent clustering –Significantly reduces the overlap and dead space A preferred structure for Datcubes storage Representation of Datacube only provide good clustering for half of the total group-bys Degradation due to strong interleaving between points of these group-bys.

Dataless & Reduced Cubetree Dataless Cubtree: Only contains aggregate values but no data values Better clustering than a full tree in a R-Tree –Projection points are not interleaved Reduced Cubetree: Each hyper-plane which containing aggregates will form a R-Tree independently The dimension of R-Tree reduced by one. Better clustering and query performance

Allocating of goupbys to R-Trees A set of group-bys are compatible if there exist a sort order that guarantees no dispersion Allocate a group-by to one of the N R-Trees –the set of group-bys for this R-Tree is compatible –if a group-by cannot find a compatible set assign it to a set that contain all of its gorup-by attributes. (false allocation) Selection of sort order for Packed R-Tree is also an import parameter for favoring some prefered group-bys

Bulk Incremental Update

Iceberg Cube Selectively compute only those partitions that satisfy an aggregate condition Aggregate with low support reveal little meaning & make the cube sparse Conditions like –Minimum support of a partition –Required Range

Bottom-Up Cube Parent to compu the child

Bottom-Up Cube (2) Starting from a bottom single dimension groupby If current inputs can be pruned return Partition the data in this group-by If a partition is greater than the minsup –recursive call on BUC with the partition as inputs Loop until all dimensions is done

Bottom-Up Cube (3) Similar idea of Apriori-gen Apriori will generate all the candidates at the same level first (breadth first) BUC is in depth first manner. –To reduce memory requirement Dimension ordering: provide better pruning –Cardinality, Skew & Correlation