CCF_100/relational
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

binary functions

Browse Source 
git-svn-id: http://galileo.dmi.unict.it/svn/relational/trunk@120 014f5005-505e-4b48-8d0a-63407b615a7c
This commit is contained in:
LtWorf 2009-04-01 14:30:19 +00:00
parent 356f4a0f10
commit 14a2cbb229
1 changed files with 42 additions and 12 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

54
complexity
View File

@ -16,6 +16,11 @@ Notation
Single letters will be used to indicate relations and letters between
| will indicate the cardinality (number of tuples) of the relation.
Number of tuples can't be enough. For example a relation with one
touple and thousands of fields, will not take O(1) in general to be
evaluated. So we assume that relations will have a reasonable and
comparable number of fields.
Then after evaluating the big O notation, an attempt to find more
precise results will be done, since it will be important to know
with a certain precision the weight of the operation.
@ -45,13 +50,6 @@ Notation
In the end we have O(|n|) as complexity for a selection on the
relation n.
The assumption made of considering constant the number of fields is
a bit strong. For example a relation could have hundreds of fields
and two tuples.
So in general, the complexity is something more like O(|n| * f) where
f is the number of the fields.
1.2 Rename
@ -60,37 +58,69 @@ Notation
The big issue is to copy the content of the relation into a new
relation object, so the new one can be modified.
So the operation depends on the size of the relation: O(|n| * f).
So the operation depends on the size of the relation: O(|n|).
1.3 Projection
The projection operation creates a copy of the original relation
using only a subset of its fields. Time for the copy is something
like O(|n|*f) where f is the number of fields to copy.
like O(|n|) where f is the number of fields to copy.
But that's not all. Since relations are set, duplicated items are not
allowed. So after extracting the wanted elements, it has to check if
the new tuple was already added to the new relation. And this brings
the complexity to O((|n|*f)²).
the complexity to O(|n|²).
2. BINARY OPERATORS
Relational defines nine binary operations, and they will be studied
in this section.
in this section. Since we will deal with two relations per operation
here, we will call them m and n, and f and g will be the number of
their fields.
2.1 Product
2.1 Product
Product is a very complex operations. It is O(|n|*|m|).
Obvious.
2.2 Intersection
Same as product even if it does a different thing. But it has to
compare every tuple from n with every tuple from m, to see if they
match, and in this case, put them in the resulting relation.
So this operation is O(|n|*|m|) as well.
2.3 Difference
Same as above:
2.4 Union
This operation first creates a new relation copying all the tuples
from one of the originating relations, then compares them all with
tuples from the other relation, and if they aren't in, they will be
added.
In fact it is same as above: O(|n|*|m|)
2.5 Thetajoin
This operation is the combination of a product and a selection. So it
is O(|n|*|m|) too.
2.6 Outher
This operation is the union of the outer left and the outer right
join. Makes it O(|n|*|m|) too.
2.7 Outher_left
O(|n|*|m|), very depending on the number of the fields, because they
are compared.
2.8 Outher_right
Mirror operation of outer_lef
2.9 Join
Same as above.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx