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functional dependencies If we are to check updates ef ciently, we should design relational-database schemas that allow update validation without the computation of joins To decide whether joins must be computed to check an update, we need to determine what functional dependencies can be tested by checking each relation individually Let F be a set of functional dependencies on a schema R, and let R1 , R2 , , Rn be a decomposition of R The restriction of F to Ri is the set Fi of all functional dependencies in F + that include only attributes of Ri Since all functional dependencies in a restriction involve attributes of only one relation schema, it is possible to test such a dependency for satisfaction by checking only one relation Note that the de nition of restriction uses all dependencies in F + , not just those in F For instance, suppose F = {A B, B C}, and we have a decomposition into AC and AB The restriction of F to AC is then A C, since A C is in F + , even though it is not in F The set of restrictions F1 , F2 , , Fn is the set of dependencies that can be checked ef ciently We now must ask whether testing only the restrictions is suf cient Let F = F1 F2 Fn F is a set of functional dependencies on schema R, but, in general, F = F However, even if F = F , it may be that F + = F + If the latter is true, then every dependency in F is logically implied by F , and, if we verify that F is satis ed, we have veri ed that F is satis ed We say that a decomposition having the property F + = F + is a dependency-preserving decomposition Figure 712 shows an algorithm for testing dependency preservation The input is a set D = {R1 , R2 , , Rn } of decomposed relation schemas, and a set F of functional dependencies This algorithm is expensive since it requires computation of F + ; we will describe another algorithm that is more ef cient after giving an example of testing for dependency preservation We can now show that our decomposition of Lending-schema is dependency preserving Instead of applying the algorithm of Figure 712, we consider an easier alternative: We consider each member of the set F of functional dependencies that we compute F + ; for each schema Ri in D do begin Fi : = the restriction of F + to Ri ; end F := for each restriction Fi do begin F = F Fi end compute F + ; if (F + = F + ) then return (true) else return (false); Figure 712 Testing for dependency preservation.

CourseNo CHAR(6), CrsDesc VARCHAR(250), CrsUnits SMALLINT, CONSTRAINT PKCourse PRIMARY KEY(CourseNo), CONSTRAINT UniqueCrsDesc UNIQUE (CrsDesc) )

$995 per probe $5,500 to $12,000 $3,000 to $12,000 per probe $4,995 for 250 nodes $1,495 for software; $2,995 to $14,995 for probe hardware

The McGraw Hill Companies, 2001

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TipOftentimes, vendors of network probes include additional capabilities in their products, over and above the standards-based capabilities These enhancements are generally proprietary, and real benefits may not be realized unless the RMON NMS (remote monitoring, Network Management System) software supports those proprietary extensions To get the most out of your monitoring system, be sure to evaluate the RMON NMS software in tandem with the hardware probes

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Some tables need more than one column in the primary key In the Enrollment table, the combination of StdSSN and OfferNo is the only candidate key Both columns are needed to identify a row A primary key consisting of more than one column is known as a composite or a combined primary key CREATE TABLE Enrollment (

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