Re: Database design

x schrieb:
"Alexandr Savinov" <spam@xxxxxxxxxxxxxxxxxxx> wrote in message
news:43fd75ce$1@xxxxxxxxxxxxxx
x schrieb:

Anyway, I do not understand why a structure without an order
(hierarchy,
multiple levels, depth etc.) cannot be characterized as flat? It is
rather precise characterization (in contrast to many terms from
academic
papers which are frequently simply misleading).
third level - the relation
second level - the tuple
first level - the value
And each value belong to a domain also.

How flat is this.

Because what you wrote is actually a definition of being flat:

You said "depth", "multiple levels".
I have shown you "multiple levels".
I don't know your "definition of being flat".

Space (say, 2-dimensional Euclidean space)
Point (in this space, as a combination of 2 coordinates)
Coordinate (a projection of the point on some axis)

The Euclidean space and a relations are not the same thing.

Yes, but under certain formal and informal assumptions we can show that they are.

Since there is no continuation (this space is not nested) we say it is
flat.

YOU keep saying that.

Yes, that is right, we are saying that.

Continuation ? At infinity ?

No. Infinity does not exist. To any desirable level. That is, the depth is not fixed. Actually we can continue to different depth along different dimension - any dimension may have its own depth (maximum level of details).

We can build a non-flat space if assume that coordinates are
themselves points with their own coordinates.

Nobody stop you to do that in the RM.

Yes, using RM we can implement a non-flat (hierarchical space).
(And not only this, but also graphs and many-many other structure.)
But the question was what we can implement using only one table. That the statement was that one table is flat.

Those coordinates could
also be points with their own coordinates and so on.

At infinity ?

To any desirable level down to the maximum depth.

Alternatively, we
can continue this space hierarchy in the opposite direction (upward).
The points from this set can be used as coordinates for points from
another set. Those points can again be used as coordinates.

Nobody stop you to do that in the RM.

Yes, RM is powerful and flexible enough to model such structures. But the question is if one table can do that.

So we call a structure flat if it can be shown equivalent to a
n-dimensional space (without a hierarchy).

You call it so. I have not seen a formal definition.
A relation is not equivalent to a n-dimensional space.
Please define the equivalence relation.

I already defined. Here it is again:

Domains = Axes
Values = Coordinates
Points = Records
Relation = N-dimensional space

If you change values of a record then you move it in this space by changing its coordinates. In the case of NULL this point does not exist along this axis (it is not visible from that perspective, is not projected on this axis).

What do you mean by "an n-dimensional space is without hierarchy" ?

Product
Vendor p1 p2 p3
v1 c1 c2 c3
v2 c4 c5 c6

has at least two hierarchies:
Vendor --> Product
Product--->Vendor

Implicitly you assume the existence of two tables while we are talking about one table only. With tables you can model two levels. With more tables you can model more levels (or more dimensions - it depends how you arrange and interpret them).

So again, the question is what can we model with a single table. Since the number of levels is limited we could find it natural to call such a structure flat. That is all.

--
http://conceptoriented.com
.

Relevant Pages

  • Re: Database design
    ... I don't know your "definition of being flat". ... can continue this space hierarchy in the opposite direction. ... A relation is not equivalent to a n-dimensional space. ... Vendor --> Product ...
    (comp.databases.theory)
  • Re: Database design
    ... "Flat" in this context means the absence of ... hierarchy, i.e., all the elements are at the same level. ... If it is the database then it could be qualified as a tree-aware database. ... If it is you then the database is of non-tree type (even if it stores trees). ...
    (comp.databases.theory)
  • Re: Simple question
    ... but it's sufficiently flat for me to ignore the variations. ... As for the variations along the Y dimension, ...
    (sci.stat.math)
  • Re: Database design
    ... "Flat" in this context means the absence of ... hierarchy, i.e., all the elements are at the same level. ... has nothing to do with n-dimensionality, i.e., n-dimensional model can ... not know that it is a tree and hence cannot help us in its use. ...
    (comp.databases.theory)
  • Latest version of glossary
    ... We could maybe add dimension, entity, flat, ... such as "XML entity" to distinquish it from the more ... any use of the term flat tends to be seen as inflammatory by ...
    (comp.databases.theory)