Primary Horizontal Fragmentation in DDBMS- Completeness of simple predicate

Question

"An important aspect of simple predicates is their completeness; another is their minimality. A set of simple predicates Pr: is said to be complete if and only if there is an equal probability of access by every application to any tuple belonging to any minterm fragment that is defined according to Pr2.

Example:- Consider the fragmentation of relation PROJ given in Example 3.8. If the only application that accesses PROJ wants to access the tuples according to the location, the set is complete since each tuple of each fragment PROJi (Example 3.8) has the same probability of being accessed. If, however, there is a second application which accesses only those project tuples where the budget is less than or equal to $200,000, then Pr is not complete. Some of the tuples within each PROJi have a higher probability of being accessed due to this second application. To make the set of predicates complete, we need to add (BUDGET <= 200000, BUDGET > 200000) to Pr:

Pr = {LOC=“Montreal”, LOC=“New York”, LOC=“Paris”, BUDGET <= 200000, BUDGET > 200000}"

I uploaded the Fig 3.3 & Example 3.8: -

Figure 3.3

Example 3.8

Now I not understand how I can know the Pr is complete or not

So What meaning of "equal probability of access by every application to any tuple belonging to any minterm fragment"

Any example how calculate equal probability for each application access any tuple ?

Bigler

Answer 1

I see this example from Principles of Distributed Database Systems by Özsu and Valduriez has been a bit unclear. Equal probability simply means that an application has no WHERE condition for which there is no separate fragment. So if there is an application fecthing tuples with the condition WHERE budget >= 200 000 you have to add (BUDGET <= 200000, BUDGET > 200000) to the set of predicates.

If you search for minterm fragments on the net you find mostly academic lecture notes and most of those notes have the same example as in the book. In real world the queries would probably use a much wider range of conditions and would result to 1001 fragments if the set should be complete (I would challenge anyone to present the practical and real-world example of the need to make a set of predicates complete).

Prefigure