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require to hold on Lending-schema, and show that each one can be tested in at least one relation in the decomposition We can test the functional dependency: branch-name branch-city assets using Branch-schema = (branch-name, branch-city, assets) We can test the functional dependency: loan-number amount branch-name using Loan-schema = (branch-name, loan-number, amount) If each member of F can be tested on one of the relations of the decomposition, then the decomposition is dependency preserving However, there are cases where, even though the decomposition is dependency preserving, there is a dependency in F that cannot be tested in any one relation in the decomposition The alternative test can therefore be used as a suf cient condition that is easy to check; if it fails we cannot conclude that the decomposition is not dependency preserving, instead we will have to apply the general test We now give a more ef cient test for dependency preservation, which avoids computing F + The idea is to test each functional dependency in F by using a modi ed form of attribute closure to see if it is preserved by the decomposition We apply the following procedure to each in F result = while (changes to result) do for each Ri in the decomposition t = (result Ri )+ Ri result = result t The attribute closure is with respect to the functional dependencies in F If result contains all attributes in , then the functional dependency is preserved The decomposition is dependency preserving if and only if all the dependencies in F are preserved Note that instead of precomputing the restriction of F on Ri and using it for computing the attribute closure of result, we use attribute closure on (result Ri ) with respect to F , and then intersect it with Ri , to get an equivalent result This procedure takes polynomial time, instead of the exponential time required to compute F +.

221 For each of the SQL aggregate functions sum, count, min and max, show how to compute the aggregate value on a multiset S1 S2 , given the aggregate values on multisets S1 and S2 Based on the above, give expressions to compute aggregate values with grouping on a subset S of the attributes of a relation r(A, B, C, D, E), given aggregate values for grouping on attributes T S, for the following aggregate functions: a sum, count, min and max b avg c standard deviation 222 Show how to express group by cube(a, b, c, d) using rollup; your answer should have only one group by clause 223 Give an example of a pair of groupings that cannot be expressed by using a single group by clause with cube and rollup 224 Given a relation S(student, subject, marks), write a query to nd the top n students by total marks, by using ranking 225 Given relation r(a, b, d, d), Show how to use the extended SQL features to generate a histogram of d versus a, dividing a into 20 equal-sized partitions (that is, where each partition contains 5 percent of the tuples in r, sorted by a)

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If you recall from 8, CWSI contains an application called TrafficDirector (it's an option element when you install CWSI) TrafficDirector is a stand-alone application that acts as a management station and collects network traffic data from remote probes and switches You can use TrafficDirector to monitor usage, troubleshoot problems, chart trends, and set alarms for severe network conditions

OfferNo INTEGER, StdSSN CHAR(11), EnrGrade DECIMAL(3,2), CONSTRAINT PKEnrollment PRIMARY KEY(OfferNo, StdSSN) ) Nonminimal superkeys are not important because they are common and contain columns that do not contribute to the uniqueness property For example, the combination of StdSSN and StdLastName is unique However, if StdLastName is removed, StdSSN is still unique Referential Integrity

The McGraw Hill Companies, 2001

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Like other probes, TrafficDirector sits centrally and queries remote probes to learn about traffic on the network Once they're initiated, these probes are called agents and can be grouped together for easier administration You can use three kinds of probes with TrafficDirector: Dedicated SwitchProbe devices These devices are purchased from Cisco ($2,000 $12,000) and come in a variety of protocol types A network analysis module This is a Cisco card you insert into a Catalyst 5000 to give it all the RMON and RMON-2 capabilities of a probe ($14,995) Cisco switches Some Cisco switches can be configured to act as probes If you have the switches, this is the most cost-effective way to create probes For switches configured to use RMON, Cisco uses what it calls mini-RMON This only obtains a limited set of statistics To get the full range of statistics in RMON and RMON-2, you will need to use a SwitchProbe or install a Network Analysis Module TipSome of Cisco's switches may not have the capability to support all the groups of RMON, but most support at least the first four groups When you're looking at buying a switch that supports RMON, be smart and dig a little deeper and find out which specific groups the switch supports

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