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is modeled as a voltage source given by v s (t) = 170 sin 377t The chord, which for our purposes transmits current to the toaster and dissipates heat, will be modeled as a resistor, which we denote as Rc In this example Rc = 20 We model the toaster by a resistor Rt = 10 Don t worry about the values of resistance given These are just for instructional purposes so that you can get a feel of doing circuit analysis; they don t necessarily re ect realistic values At time t = 0, the switch is closed and the toaster starts operation Draw the circuit model and nd the current that ows through the toaster together with the voltages across each resistor SOLUTION We draw the elements as a series circuit, the wall outlet connected to the chord that is connected to the switch that is connected to the resistor representing the toaster This is shown in Fig 2-9 To solve the problem, imagine the switch closing to make a complete circuit There is only one loop to worry about in this circuit, so applying KVL in a

the number of strategies for our simple example may be large Query optimization by exhaustive enumeration of all alternative strategies may not be practical in such situations Fragmentation transparency implies that a user may write a query such as branch-name = Hillside (account) Since account is de ned as account1 account2 the expression that results from the name translation scheme is branch-name = Hillside (account1 account2 ) Using the query-optimization techniques of 13, we can simplify the preceding expression automatically The result is the expression branch-name = Hillside (account1 ) branch-name = Hillside (account2 ) which includes two subexpressions The rst involves only account1 , and thus can be evaluated at the Hillside site The second involves only account2 , and thus can be evaluated at the Valleyview site There is a further optimization that can be made in evaluating branch-name = Hillside (account1 ) Since account1 has only tuples pertaining to the Hillside branch, we can eliminate the selection operation In evaluating branch-name = Hillside (account2 ) we can apply the de nition of the account2 fragment to obtain branch-name = Hillside ( branch-name = Valleyview (account)) This expression is the empty set, regardless of the contents of the account relation Thus, our nal strategy is for the Hillside site to return account1 as the result of the query

As we saw in 13, a major decision in the selection of a query-processing strategy is choosing a join strategy Consider the following relational-algebra expression: account

.

Assume that the three relations are neither replicated nor fragmented, and that account is stored at site S1 , depositor at S2 , and branch at S3 Let SI denote the site at which the query was issued The system needs to produce the result at site SI Among the possible strategies for processing this query are these:

20

The McGraw Hill Companies, 2001

Ship copies of all three relations to site SI Using the techniques of 13, choose a strategy for processing the entire query locally at site SI Ship a copy of the account relation to site S2 , and compute temp1 = account 1 depositor at S2 Ship temp1 from S2 to S3 , and compute temp2 = temp1 1 branch at S3 Ship the result temp2 to SI Devise strategies similar to the previous one, with the roles of S1 , S2 , S3 exchanged No one strategy is always the best one Among the factors that must be considered are the volume of data being shipped, the cost of transmitting a block of data between a pair of sites, and the relative speed of processing at each site Consider the rst two strategies listed If we ship all three relations to SI , and indices exist on these relations, we may need to re-create these indices at SI This re-creation of indices entails extra processing overhead and extra disk accesses However, the second strategy has the disadvantage that a potentially large relation (customer 1 account) must be shipped from S2 to S3 This relation repeats the address data for a customer once for each account that the customer has Thus, the second strategy may result in extra network transmission compared to the rst strategy

Suppose that we wish to evaluate the expression r1 1 r2 , where r1 and r2 are stored at sites S1 and S2 , respectively Let the schemas of r1 and r2 be R1 and R2 Suppose that we wish to obtain the result at S1 If there are many tuples of r2 that do not join with any tuple of r1 , then shipping r2 to S1 entails shipping tuples that fail to contribute to the result We want to remove such tuples before shipping data to S1 , particularly if network costs are high A possible strategy to accomplish all this is: 1 Compute temp1 R1 R2 (r1 ) at S1 2 Ship temp1 from S1 to S2 3 Compute temp2 r2 5 Compute r1