Calculation of the order in which the GROUP-BYs are created depends on
the cost of deriving a lower order (one with a lower number of
attributes) group-by from a higher order (also called the
parent) group-by. For example, between ABD 
BD and BCD
BD one needs to select the one with the lower cost. Cost
estimation of the aggregation operations can be done by establishing a
cost model. Some calculations do not involve communication and are
local, others involving communication are labeled as non-local.
Details of these techniques for a parallel implementation using
multidimensional arrays can be found in [GC97a].
For higher dimensions and sparse data sets, a chunk based implementations
using BESS needs to determine the order in which chunks are accessed.
To reduce disk I/O, chunk reuse has to be maximized. During aggregation,
both source and destination chunks can be reused. The aggregation order
can either be a depth-first traversal of the DAG or a
breadth-first traversal. Each of these can be either done at the
individual cube reuse level or at the chunk reuse level, thus resulting in
4 different schedules. At the cube reuse level, a child cube is calculated from
the parent by aggregating each chunk of the parent along the aggregation dimension,
in a pipelined manner.
For a depth-first traversal this would result in the following
order of calculation ABCD ABC AB A,
and then other calculations from ABCD and so on.
Similarly, for a breadth-first traversal, ABCD ABC,
ABCD ABD, ABCD ACD, ABCD BCD are
materialized and then other calculations from ABC and so on.
In a chunk-reuse mechanism, the order of calculations are the same but this order is followed on a chunk by chunk basis. We are evaluating these for the effect of various optimizations on performance and results of these will be presented at the conference.