Some database applications require you to perform a series of actions
where you know only that some actions must be performed before others.
Before you can perform the actions, you must work out a safe sequence
that takes into account all of the dependencies. This week in The
Database Programmer we will see an algorithm for doing this.
Examples
There are many examples where a programmer must work out dependencies
before doing something.
A manufacturing package may track many steps in the manufacture of an
item. Some steps cannot be performed until others are complete. A
simple system would require the end-user to work out the entire process,
but a better system would let the user enter only the dependencies: which
processes require others to be complete. In this kind of system the
computer can be used to schedule manufacturing tasks.
All popular Linux distributions have a package installation system in
which each package lists its required dependencies. If you want to install
a large number of packages in one shot, producing a tangled bunch of
related dependencies, today's algorithm can be used to work them all out.
If you are using a data dictionary to build tables, every foreign key
represents a dependency, where the child table requires the parent table
to exist before it can be built. Today's algorithm can be used to
sequence the tables and build them in order.
Another database example is generating code to perform calculations.
Some calculations will depend on previous calculations, so your code
generator must be able to sequence them all so that the calculations
are performed in the proper order.
Big Words: Directed Acyclic Graph
The examples abvoe are all cases of what mathematicians call a "http://en.wikipedia.org/wiki/Directed_acyclic_graph"
>Directed Acyclic Graph. If you do not want to read the entire
Wikipedia article, the main points are these:
- We have a set of items. These can be anything you are keeping
track of in your database.
- Any item may be connected to zero or more other items.
- The connection is one-way only. So if we say A requires B, we are
not saying that B also requires A (in fact it is forbidden).
- There can be no loops (cycles). If A requires B, B may not require A.
Further, if A requires B, and B requires C, C may not require A.
Whenever I can, I like to point out that it is very useful to read up
on the mathematical foundations of certain programming techniques.
We can often pick up very useful insights from those who think of these
things at the most abstract level. It is also much easier to get
advice from the more abstract-minded database people if you are at least
marginally familiar with the mathematical terms.
The Tables
So now let us proceed to the tables and the code. The tables below
show a data dictionary that will be used to generate DDL to build
a database:
Table: TABLES
TABLE | DESCRIPTION | SEQUENCE
------------+------------------------+---------
ORDERS | Sales Orders Headers | ?
ORDER_LINES | Sales order lines | ?
CUSTOMERS | Customers | ?
ITEMS | Items | ?
Table: DEPENDENCIES
CHILD_TABLE | PARENT_TABLE
-------------+---------------
ORDERS | CUSTOMERS
ORDER_LINES | ORDERS
ORDER_LINES | ITEMS
The problem here is knowing the safe order in which to build the
tables. If I try to build ORDER_LINES before I have built ITEMS,
then I cannot put a foreign key onto ORDER_LINES, because ITEMS is
not there. In short, I need to know the value of the SEQUENCE
column in the example above.
The Expected Answer
The example above is simple enough that we can work it out by hand.
This is actually a good idea, because we want to get an idea of what
the answer will look like:
TABLE | DESCRIPTION | SEQUENCE
------------+------------------------+---------
ORDERS | Sales Orders Headers | 1
ORDER_LINES | Sales order lines | 2
CUSTOMERS | Customers | 0
ITEMS | Items | 0
This answer should be self-explanatory, except maybe for the fact that
both CUSTOMERS and ITEMS have the same value. We need to look at that
before we can see the code that produces it. Is it OK that two entries
have the same value, and how would our program handle that?
The short answer is that it is perfectly OK and natural for two or more
entries to have the same value. All this means is that they can be done
in any order relative to each other, so long as they are done
before the other entries.
In terms of the example, where we want to build these tables in a
database, it means that:
- We would query the list of tables and sort by SEQUENCE
- We would loop through and build each table
- We don't care about ITEMS and CUSTOMERS having the same value,
they get built
in whatever which-way the server gives us the list.
The same concept applies to the other potential examples: manufacturing,
software packages, and generating calculations. So long as you follow
the sequence, we don't care about items that have the same value.
Stating the Solution in Plain English
We are now ready to work out a program that will generate the SEQUENCE
column. The basic steps the program must perform are:
- Initialize the column to -1. A value of -1 means "Not sequenced."
- Update the column to zero for all items that have no dependencies.
- Repeat the following action until the affected rows are zero:
Update the SEQUENCE column to 1 (then 2, then 3) for all rows
that have all of their dependencies sequenced already.
- Once the command in step 3 is no longer affecting any rows,
check for any rows that have -1, these are involved in
circular dependencies and we cannot proceed until the
user straightens them out.
Stating the Solution in Code
The first step is very easy, we initialize the table with this command:
UPDATE TABLES SET SEQUENCE = -1;
The next step is also very easy, we mark with a '0' all of the
tables that have no dependencies. The basic idea is to find all of the
entries that have no entries in DEPENDENCIES.
UPDATE TABLES SET SEQUENCE = 0
WHERE NOT EXISTS (SELECT child FROM DEPENDENCIES
WHERE child = TABLES.TABLE)
Now for the hard part. We now have to execute a loop. On each pass
of the loop we are looking for all items whose dependencies have
all been sequenced. We will do this over and over until the command
is not affecting any rows. It is important that we cannot exit the
loop by testing if all rows are sequenced, because a circular dependency
will prevent this from happening and we will have an infinite loop.
You can control this loop from client code, but I wrote mine as a
Postgres stored procedure. This algorithm turns out to be surprisingly
complicated. The UPDATE command below may not be all that
self-explanatory. What it works out is:
- Get a list of child tables from the DEPENDENCIES table
- JOIN through to TABLES to look at the SEQUENCE value
of their parents.
- Group and check that the minimum value is greater than zero, if
it is it means all parents are sequenced and the table can
be sequenced.
- Update the SEQUENCE value for the tables we found
CREATE OR REPLACE FUNCTION zdd.Table_Sequencer() RETURNS void AS
$BODY$
DECLARE
-- Note that rowcount is initialized to be > 0, this makes
-- the loop work properly
rowcount integer := 1;
-- This tracks the value we are assigning to SEQUENCE. We
-- initialize it to 1 because we already took care of the
-- the rows that have value 0
lnSeq integer := 1;
BEGIN
while rowcount > 0 LOOP
UPDATE tables set SEQUENCE = lnSeq
FROM (SELECT t1.CHILD
FROM DEPENDENCIES t1
JOIN TABLES t2 ON t1.PARENT = t2.TABLE
GROUP BY t1.CHILD
HAVING MIN(t2.SEQUENCE) >= 0
) fins
WHERE TABLES.TABLE = fins.CHILD
AND TABLES.SEQUENCE = -1;
lnSeq := lnSeq + 1;
GET DIAGNOSTICS rowcount = ROW_COUNT;
END LOOP;
RETURN;
END;
$BODY$
LANGUAGE plpgsql;
The stored procedure above will stop executing once the UPDATE command
is no longer having any effect. Once that happens, your final step is
to make sure that all rows have a valid SEQUENCE value, which is to say
that no entry has SEQUENCE of -1. If any of the rows have that value
then you have a circular dependency. You must report those rows to
the user, and you can also report the dependencies that are causing
the loop.
Conclusion
Sequencing dependencies is a fundamental algorithm that has a lot of
use cases in database applications. It is easy enough to accomplish,
but the innermost UPDATE command can be a little puzzling when you
first look at it. Once you have mastered this algorithm you are on
the way to the "big leagues" of database applications such as ERP,
MRP and others.
Next Essay: "http://database-programmer.blogspot.com/2008/09/advanced-table-design-secure-password.html"
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