Applying OLAP Pre-Aggregation Techniques to ... - Jacobs University

4.2 Cost Model 69
Cost of independent pre-aggregates
The cost of retrieving the results of independent pre-aggregates (C IP AS ) is given by:
C IP AS (Q, T ) = C fin (Q, T ) +
∑
|IP AS|
i=0
C acc (p i ) (4.8)
where C fin is the cost of finding the pre-aggregates ∈ IP AS in the pre-aggregated
pool T , and C acc is the accumulated cost of retrieving the results of the pre-aggregates.
Cost of overlapped pre-aggregates
The cost of retrieving the results of overlapped pre-aggregates (C OP AS ) is given by:
C OP AS (Q) = C fin (Q, T ) +
∑
|OP AS|
i=0
|S|
∑
C dec (p i ) + C r (s i ) (4.9)
where C fin is the cost of finding the pre-aggregates ∈ OP AS in the pre-aggregated
pool T , C dec is the cost of decomposing the spatial domain of each pre-aggregate into
a set of sub-partitions S such that the spatial domain of the partitioned pre-aggregate
corresponds to p i.sdom − (p i.sdom ∩ Q), and C r is the cost of aggregating each resulting
sub-partition s i ∈ S from raw data.
Cost of aggregating sub-partitions of a query
The cost of aggregating all sub-partitions forming a query is given by:
|SP |
∑
C SP (Q) = C dec (Q) + C r (s i ), (4.10)
where C dec is the cost of decomposing Q into a set SP of sub-partitions, and C r is
the cost of aggregating each resulting sub-partition s ∈ SP from raw data. Note that
C dec is influenced by the costs of accessing the tiles required to aggregate each subpartition,
and the cost of accessing the spatial properties of the pre-aggregates in IPAS
and OPAS.
4.2.3 Computing Queries from Dominant Pre-Aggregates
The cost of computing an aggregate query Q using a dominant pre-aggregate is
given by:
C DP AS (Q) = C DP (Q, T ) + C agg (p cd ), (4.11)
where C DP is the sum of the cost of finding the pre-aggregates ∈ DPAS in the preaggregated
pool T and the cost of finding the closest dominant pre-aggregate p cd ,
and C agg is the cost of computing the aggregate difference of p cd corresponding to
p cd.sdom − Q .sdom .
i=0
i=0