Slideshow:
Important property of operators that are
both
commutative and
associative
The ⋈ (and ×) operators that are
both
commutative and
associative !!
- Property:
- If an operator is both communitative and associative, an operation involving multiple operands can be carried out in any ordering of the operands
- Consider the
+ operator that is
both
communitative and
associative:
2 + 3 + 6 = 3 + 2 + 6 = 3 + 6 + 2 = 6 + 3 + 2 = ...
- In fact, the
operator
behaves
as if can accept
multiple operands:
- From the previous 2 webpages,
we know that:
- ⋈ and × are both cummunitative and associative
- This fact
provides use an
opportunity to
optimize a
query:
- Different ordering in the execution of the ⋈ operation can produce different intermediate results (often with large difference in size of result sets) !!!
- So one of the
topics (problems) in
query optimization will be:
- Find the
optimal join ordering
of a set of
⋈ operations...
(later !!!)
- Find the
optimal join ordering
of a set of
⋈ operations...