Query Evaluation

SQL to ERA• SQL queries are translated into extended relational algebra.

• Query evaluation plans are represented as trees of relational operators, with labels identifying the algorithm to use at each node. – Thus, relational operators serve as building blocks for evaluating

queries.

– Implementation of these operators is carefully optimized for good performance.

– Algorithms for individual operators can be combined in many ways to evaluate a query.

• The process of finding a good evaluation plan is called query optimization.

Running Example – AirlineEmployees (sin INT, ename VARCHAR(20), rating INT, age REAL)

Maintenances (sin INT, planeId INT, day DATE, descCode CHAR(10))

• Assume that – each tuple of Maintenances is 40 bytes long

– a block can hold 100 Maintenances tuples (4K block)

– we have 1000 blocks of such tuples.

• Assume that – each tuple of Employees is 50 bytes long,

– a block can hold 80 Employees tuples

– we have 500 blocks of such tuples.

An SQL query and its RA equiv.SELECT ename

FROM Employees, Maintenances

WHERE Employees.SIN = Maintenances.SIN AND

Maintenances.planeId = 100 AND

Employees.rating > 5;

ename (planeId=100 AND rating>5 (Employees Maintenances))

ename

planeId=100 AND rating>5

Maintenances Employees

RA expressions can be represented by an

expression tree.

An algorithm is chosen for each node in the

expression tree.

Notions of clustering

• Clustered file: e.g. store movie tuples together with the corresponding studio tuple.

• Clustered relation: tuples are stored in blocks mostly devoted to that relation.

• Clustering index: tuples (of the relation) with same search key are stored together as controlled by the index.

Algorithms for selection • Given a selection R.attr = value (R), if there is no index on R.attr,

then we have to scan R. – How many disk accesses if R is the Maintenances relation?

– On average 1000/2 block (pages) reads.

• If there is an index we have to typically do 3 disk accesses– This is, assuming a non-clustering B-Tree with 3 levels, with the

root in main memory.

• Given a selection R.attr < value (R)

– Even when there is a non-clustering index we might better scan the relation ignoring the index. Why?

– Of course, if we have a clustering index, we use it.

Algorithms for projections• Given a projection we have to scan the relation and drop certain

fields of each tuple.– That’s easy.

• However, if we need to do a set projection (as opposed to bag projection) specified with the DISTINCT keyword in SQL, we need to remove duplicates.– This is more expensive.

– Usually done by sorting, in order to co-locate the duplicates and then remove them.

– Can be combined with the final pass of sorting.

Algorithms for joins• Joins are expensive operations and very common.

– They have been widely studied, and systems typically support several algorithms to carry out joins.

• Consider the join of Maintenances and Employees, with the join condition Employees.SIN=Maintenance.SIN.

• Suppose that one of the tables, say Employees, has an index (B-Tree) on the SIN column.

• We can scan Maintenances and, for each tuple, use the index to probe Employees for matching tuples.

• This approach is called index nested loops join.

• It takes about 3 I/Os on average to retrieve the appropriate page of the index. – For each of the 100,000 maintenance records we try to access the

corresponding employee with 3 I/Os.

– So, 100,000*3 = 300,000 I/Os on average!!

Algorithms for joins (sort-merge)• Another algorithm is to sort both tables on the join column,

and then scan them to find matches. This is called sort-merge join.

• Assuming that we can sort Maintenances in two passes, and Employees in two passes as well, let us consider the cost of sort-merge join.

• Because we read and write Maintenances in each pass, the sorting cost is 2 * 2 * 1000 = 4000 I/Os.

• Similarly, we can sort Employees at a cost of 2 * 2 * 500 = 2000 I/Os.

• In addition, the second phase of the sort-merge join algorithm requires an additional scan of both tables.

• Thus the total cost is 4000+ 2000+ 1000+ 500= 7500 I/Os. (Much better!!)

Algorithms for joins (sort-merge)So, we have:• index nested loops join: 300,000 I/Os• sort-merge join : 7,500 I/Os.

• Why bother with index nested loops join?• Well, “index nested loops” method has the nice property that it is incremental.

– The cost of our example join is incremental in the number of Maintenances tuples that we process.

– Therefore, if some additional selection in the query allows us to consider only a small subset of Maintenances tuples, we can avoid computing the join of Maintenances and Employees in its entirety.

– For instance, suppose that we only want the result of the join for the plane 100, and there are very few such maintenances.

– For each such Maintenances tuple, we probe Employees, and we are done. • If we use sort-merge join, on the other hand, we have to scan the entire

Maintenances table at least once, and the cost of this step alone is likely to be much higher than the entire cost of index nested loops join.

Query Optimization• Observe that the choice of index nested loops join is based on

considering the query as a whole, including the extra selection on Maintenances, rather than just the join operation by itself.

• This leads us to the next topic, query optimization, which is the process of finding a good plan for an entire query.

• Query optimization is one of the most important tasks of a relational DBMS. The optimizer generates alternative plans and chooses the plan with the least estimated cost.

Query evaluations plans• Recall: A query evaluation plan consists of an extended relational algebra

tree, with additional annotations at each node indicating the implementation method to use for each relational operator.

ename (on the fly)

planeId=100 AND rating>5 (on the fly)

(file scan) Employees Maintenances (file scan)

(nested loops)

Method to use

Sometimes it might be possible, to pipeline the result of one operator to another operator without creating a temporary tablefor the intermediate result. This saves in cost.When the input to a unary operator (e.g. or ) is pipelined into it, we say the operator is applied on-the-fly.

Alternative query evaluation plans• Let’s look at two (naïve plans)

ename (on the fly)

planeId=100 AND rating>5 (on the fly)

Maintenances(file scan)

Employees(file scan)

(nested loops join)

ename (on the fly)

planeId=100 AND rating>5 (on the fly)

Maintenances(file scan)

Employees(file scan)

(sort merge join)

Cost for this plan:

300,000 I/Os for the join.

and are done in the fly; no I/O cost for them.

Cost for this plan:

7,500 I/Os for the join.

and are done in the fly; no I/O cost for them.

We don’t consider the cost for writing the final result, since it is the same for any plan.

Plan: Pushing selections I• Good heuristic for joins is to

reduce the sizes of the tables to be joined as much as possible. – One approach is to apply

selections early; if a selection operator appears after a join operator, it is worth examining whether the selection can be

'pushed' ahead of the join. • As an example, the selection

planeId=100 involves only the attributes of Maintenances and can be applied to Maintenances before the join.

• Similarly, the selection rating>5 involves only attributes of Employees and can be applied to Employees before the join.

ename (on the fly)

planeId=100

Maintenances(file scan)

Employees(file scan)

rating>5

(sort-merge join)

(scan write to temp T2)

(scan write to temp T1)

Plan: Pushing selections II• The cost of applying

planeId=100 to Maintenances is: – the cost of scanning

Maintenances (1000 blocks) plus

– the cost of writing the result to a temporary table Tl.

• To estimate the size of T1, we reason as follows: – if we know that there are 100

planes, we can assume that maintenances are spread out uniformly across all planes and estimate the number of blocks in T1 to be 1000/100 = 10.

• I.e. 1000+10 = 1010 I/Os.

ename (on the fly)

planeId=100

Maintenances(file scan)

Employees(file scan)

rating>5

(sort-merge join)

(scan write to temp T2)

(scan write to temp T1)

Plan: Pushing selections III• The cost of applying rating> 5

to Employees is: – the cost of scanning Employees

(500 blocks) plus

– the cost of writing out the result

to a temporary table, say, T2.

• If we assume that ratings are uniformly distributed over the range 1 to 10, we can approximately estimate the size of T2 as 250 blocks.

• I.e. 500 + 250 = 750 I/Os

ename (on the fly)

planeId=100

Maintenances(file scan)

Employees(file scan)

rating>5

(sort-merge join)

(scan write to temp T2)

(scan write to temp T1)

Plan: Pushing selections IV• To do a sort-merge join of T1 and

T2, they are first completely sorted and then merged.

• Assume we do that in two passes for each one. Thus, – the cost of sorting T1 is 2

* 2 * 10 = 40 I/Os. – the cost of sorting T2 is 2

* 2 * 250 = 1000 I/Os.• To merge (for the join) the sorted

versions of T1 and T2, we need to scan these tables:– the cost of this step is

10+250=260 I/Os.

• The final projection is done on-the-fly, and by convention we ignore the cost of writing the final result.

• The total cost of the plan shown is:– (1010+750)+(40+1000+260) =

3060 I/Os

And this is much better compared to the other previous plans.

ename (on the fly)

planeId=100

Maintenances(file scan)

Employees(file scan)

rating>5

(sort-merge join)

(scan write to temp T2)

(scan write to temp T1)

Pushing projections• A further refinement is to push projections, just like we pushed

selections past the join. • Observe that only the SIN attribute of T1 and the SIN and ename

attributes of T2 are really required. • When we scan Maintenances and Employees to do the

selections, we could also eliminate unwanted columns. – This on-the-fly projection reduces the sizes of the temporary tables

T1 and T2. – The reduction in the size of T1 is substantial because only an

integer field is retained. – In fact, T1 now fits within three blocks (and be all can be in MM),

and we can perform a block nested loops join with a single scan of T2.

– The cost of the join step drops to under 250 page I/Os, and the total cost of the plan drops to about 2000 I/Os.

Plan using Indexes I• Suppose that we have a

clustering B-Tree index on the planeId field of Maintenances and another B-Tree index on the SIN field of Employees.

• We can use the plan in the figure.

ename (on the fly)

planeId=100

Maintenances(clustering indexon planeId)

Employees(indexon SIN)

rating>5 (on the fly)

(Index nested loopswith pipelining )

(Use clustering index, don’t write results to temp)

Plan using Indexes II• Assume that there are 100

planes and assume that the maintenances are spread out uniformly across all planes.

– We can estimate the number of selected tuples to be 100,000/100=1000.

– Since the index on planeId is clustering, these 1000 tuples appear consecutively and therefore, the cost is:

– 10 blocks I/Os + 2 I/Os for finding the first block via the index.

ename (on the fly)

planeId=100

Maintenances(clustering indexon planeId)

Employees(indexon SIN)

rating>5 (on the fly)

(Index nested loopswith pipelining )

(Use clustered index, don’t write results to temp)

Plan using Indexes III• For each selected tuple, we

retrieve matching Employees tuples using the index on the SIN field;

• The join field SIN is a key for Employees. Therefore, at most one Employees tuple matches a given Maintenances tuple. – The cost of retrieving this

matching tuple is 3 I/Os.– So, for the 1000 Maintenances

tuples we get 3000 I/O’s.

• For each tuple in the result of the join, we perform the selection rating>5 and the projection of ename on-the-fly.

• So, total: 3000+12 = 3012 I/Os.

ename (on the fly)

planeId=100

Maintenances(clustering indexon planeId)

Employees(indexon SIN)

rating>5 (on the fly)

(Index nested loopswith pipelining )

(Use clustered index, don’t write results to temp)

Plan using Indexes IV• Why didn’t we push the selection

rating>5 ahead of the join?

• Had we performed the selection before the join, the selection would involve scanning Employees (since no index is available on the rating field of Employees).

• Also, once we apply such a selection, we have no index on the SIN field of the result of the selection.

• Thus, pushing selections ahead of joins is a good heuristic, but not always the best strategy. – Typically, the existence of useful

indexes is the reason a selection is not pushed.

ename (on the fly)

planeId=100

Maintenances(clustering indexon planeId)

Employees(indexon SIN)

rating>5 (on the fly)

(Index nested loopswith pipelining )

(Use clustered index, don’t write results to temp)

Plan using Indexes V• What about this different plan?

• The estimated size of T would be the number of blocks for the 1,000 Maintenances tuples that have planeId=100.

– i.e. T is 10 blocks.• The cost of planeId=100 as before is

12 I/Os to retrieve plus 10 additional I/Os I/Os to write T.

• Then, sort T on the SIN attribute. 2passes = 40 I/Os.

• Employees is already sorted since it has a clustering index on SIN.

• The merge phase of the join needs a scan of both T and Employees. So, 10+500=510 I/Os.

• Total: (12+10)+40+510 = 572 I/Os

ename (on the fly)

planeId=100

Maintenances(clustering indexon planeId)

Employees(clust. indexon SIN)

rating>5 (on the fly)

(sort-merge join)(Use clustering index, write results to temp T)

This improved plan also demonstrates that pipelining is not always the best strategy.