Cube Tree

1
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

2
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.

3
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

4
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

5
Bulk Incremental Update
6
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

7
Bottom-Up Cube
Parent to compu the child
8
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

9
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