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Laws involving duplicate elimination (δ)

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Slideshow:

Laws involving duplicate elimination (δ)
 
Graphically illustrated:

Laws involving duplicate elimination (δ)
 
Comments:
You can apply these law to remove duplicate tuples earlier and reduce the number of tuples However: the cost saving resulting from pushing down δ is usually small. Pushing down δ is often omitted ...
"Self-disappearing" δ operation
 
Apply δ on a set (= with no duplicates) is useless:

3 situations where tuples in a set are unique

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• Laws about δ (= duplicate elimination operator)
  • δ can usually be performed earlier in an relational algebra expression:

    Graphically depiction of the effect of these laws:

    You can see that δ is pushed down into the logical query plan/tree:

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  • Comment:

    The cost saving resulting from pushing down δ is usually small. Pushing down δ is often omitted ...

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  • Note:

    The result of δ (= duplicate elimination) is always a set (i.e.: no duplicates) !!!

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• "Self-disappearing" δ operation
  • Obvious fact:

    If R is a set (= no duplicates), then: δ(R) = R i.e.: you can drop/remove the δ operator !!!

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  • Some situations where a relation R is a set:

    R has a key (very common !!!) R = output of a grouping operation γL Each group is unique !!! Example: R = output of a set operation such as ∩Set

    In any of these situations, we can eliminate the δ operation