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A3 (primary index, equality on key) For an equality comparison on a key attribute with a primary index, we can use the index to retrieve a single record that satis es the corresponding equality condition If a B+ -tree is used, the cost of the operation, in terms of I/O operations, is equal to the height of the tree plus one I/O to fetch the record A4 (primary index, equality on nonkey) We can retrieve multiple records by using a primary index when the selection condition speci es an equality comparison on a nonkey attribute, A The only difference from the previous case is that multiple records may need to be fetched However, the records would be stored consecutively in the le since the le is sorted on the search key The cost of the operation is proportional to the height of the tree, plus the number of blocks containing records with the speci ed search key A5 (secondary index, equality) Selections specifying an equality condition can use a secondary index This strategy can retrieve a single record if the equality condition is on a key; multiple records may get retrieved if the indexing eld is not a key In the rst case, only one record is retrieved, and the cost is equal to the height of the tree plus one I/O operation to fetch the record In the second case each record may be resident on a different block, which may result in one I/O operation per retrieved record The cost could become even worse than that of linear search if a large number of records are retrieved If B+ -tree le organizations are used to store relations, records may be moved between blocks when leaf nodes are split or merged, and when records are redistributed If secondary indices store pointers to records physical location, the pointers will have to be updated when records are moved In some systems, such as Compaq s Non-Stop SQL System, the secondary indices instead store the key value in the B+ -tree le organization Accessing a record through a secondary index is then even more expensive since a search has to be performed on the B+ -tree used in the le organization The cost formulae described for secondary indices will have to be modi ed appropriately if such indices are used.

Consider a selection of the form A v (r) We can implement the selection either by using a linear or binary search or by using indices in one of the following ways: A6 (primary index, comparison) A primary ordered index (for example, a primary B+ -tree index) can be used when the selection condition is a comparison For comparison conditions of the form A > v or A v, a primary index on A can be used to direct the retrieval of tuples, as follows For A v, we look up the value v in the index to nd the rst tuple in the le that has a value of A = v A le scan starting from that tuple up to the end of the le returns

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The McGraw Hill Companies, 2001

all tuples that satisfy the condition For A > v, the le scan starts with the rst tuple such that A > v For comparisons of the form A < v or A v, an index lookup is not required For A < v, we use a simple le scan starting from the beginning of the le, and continuing up to (but not including) the rst tuple with attribute A = v The case of A v is similar, except that the scan continues up to (but not including) the rst tuple with attribute A > v In either case, the index is not useful A7 (secondary index, comparison) We can use a secondary ordered index to guide retrieval for comparison conditions involving <, , , or > The lowestlevel index blocks are scanned, either from the smallest value up to v (for < and ), or from v up to the maximum value (for > and ) The secondary index provides pointers to the records, but to get the actual records we have to fetch the records by using the pointers This step may require an I/O operation for each record fetched, since consecutive records may be on different disk blocks If the number of retrieved records is large, using the secondary index may be even more expensive than using linear search Therefore the secondary index should be used only if very few records are selected

Now we add up the current sources to obtain a single current source given by I = G 1 V1 + G 2 V2 = The total conductance is G = G1 + G2 = 1 1 7 + = 3 4 12 29 5 3 + = 3 4 12

So far, we have considered only simple selection conditions of the form A op B, where op is an equality or comparison operation We now consider more complex selection predicates Conjunction: A conjunctive selection is a selection of the form 1 2 n (r) Disjunction: A disjunctive selection is a selection of the form 1 2 n (r) A disjunctive condition is satis ed by the union of all records satisfying the individual, simple conditions i Negation: The result of a selection (r) is the set of tuples of r for which the condition evaluates to false In the absence of nulls, this set is simply the set of tuples that are not in (r) We can implement a selection operation involving either a conjunction or a disjunction of simple conditions by using one of the following algorithms: A8 (conjunctive selection using one index) We rst determine whether an access path is available for an attribute in one of the simple conditions If one

The McGraw Hill Companies, 2001