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A drawback of cost-based optimization is the cost of optimization itself Although the cost of query processing can be reduced by clever optimizations, cost-based optimization is still expensive Hence, many systems use heuristics to reduce the number of choices that must be made in a cost-based fashion Some systems even choose to use only heuristics, and do not use cost-based optimization at all An example of a heuristic rule is the following rule for transforming relationalalgebra queries: Perform selection operations as early as possible A heuristic optimizer would use this rule without nding out whether the cost is reduced by this transformation In the rst transformation example in Section 143, the selection operation was pushed into a join We say that the preceding rule is a heuristic because it usually, but not always, helps to reduce the cost For an example of where it can result in an increase in cost, consider an expression (r 1 s), where the condition refers to only attributes in s The selection can certainly be performed before the join However, if r is extremely small compared to s, and if there is an index on the join attributes of s, but no index on the attributes used by , then it is probably a bad idea to perform the selection

The McGraw Hill Companies, 2001

14

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In (65), s is just a dummy variable of integration Let s see how this equation works with some examples

early Performing the selection early that is, directly on s would require doing a scan of all tuples in s It is probably cheaper, in this case, to compute the join by using the index, and then to reject tuples that fail the selection The projection operation, like the selection operation, reduces the size of relations Thus, whenever we need to generate a temporary relation, it is advantageous to apply immediately any projections that are possible This advantage suggests a companion to the perform selections early heuristic: Perform projections early It is usually better to perform selections earlier than projections, since selections have the potential to reduce the sizes of relations greatly, and selections enable the use of indices to access tuples An example similar to the one used for the selection heuristic should convince you that this heuristic does not always reduce the cost Drawing on the equivalences discussed in Section 1431, a heuristic optimization algorithm will reorder the components of an initial query tree to achieve improved query execution We now present an overview of the steps in a typical heuristic optimization algorithm You can understand the heuristics by visualizing a query expression as a tree, as illustrated in Figure 143 1 Deconstruct conjunctive selections into a sequence of single selection operations This step, based on equivalence rule 1, facilitates moving selection operations down the query tree 2 Move selection operations down the query tree for the earliest possible execution This step uses the commutativity and distributivity properties of the selection operation noted in equivalence rules 2, 7a, 7b, and 11 For instance, this step transforms (r 1 s) into either (r) 1 s or r 1 (s) whenever possible Performing value-based selections as early as possible reduces the cost of sorting and merging intermediate results The degree of reordering permitted for a particular selection is determined by the attributes involved in that selection condition 3 Determine which selection operations and join operations will produce the smallest relations that is, will produce the relations with the least number of tuples Using associativity of the 1 operation, rearrange the tree so that the leaf-node relations with these restrictive selections are executed rst This step considers the selectivity of a selection or join condition Recall that the most restrictive selection that is, the condition with the smallest selectivity retrieves the fewest records This step relies on the associativity of binary operations given in equivalence rule 6 4 Replace with join operations those Cartesian product operations that are followed by a selection condition (rule 4a) The Cartesian product operation is often expensive to implement since r1 r2 includes a record for each combination of records from r1 and r2 The selection may signi cantly reduce the number of records, making the join much less expensive than the Cartesian product.

The McGraw Hill Companies, 2001