Evaluation of Relational Operations

Database Systems/comp4910/spring2003 1

Evaluation of Relational Operations

• Why does a DBMS implements several algorithms for each algebra operation?

• What are query evaluation plans and how are they represented?

• Why is it important to find good evaluation plan for a query? How is this done in relational DBMS?


System CatalogsFor each index:

– name, structure (e.g., B+ tree) and search key fields

For each relation( table ):– name, file name, file structure (e.g., Heap file)– attribute name and type, for each attribute– index name, for each index– integrity constraints

For each view:– view name and definition

Plus statistics, authorization, buffer pool size, Page size etc.

Catalogs are themselves stored as relations!


The following information is commonly stored

Cordinality: (NTuples(R)) -#of tupelws for each table RSize: (NPages(R)) - # of pagesIndex Cordiality: (NKyes(I)) - # of distinct key values for each index IIndex size: ( INPages(I)) - # of pages for each index IIndex Height: ( IHeight(I)) - # of nonleaf levelsIndex Range: ( ILow(I) , and IHeigh(I) ) minimume

and maximum value of present keysThe Catalog also contains information about users, - account information's and authorizations


Attr_Cat(attr_name, rel_name, type, position)

attr_name rel_name type positionattr_name Attribute_Cat string 1rel_name Attribute_Cat string 2type Attribute_Cat string 3position Attribute_Cat integer 4sid Students string 1name Students string 2login Students string 3age Students integer 4gpa Students real 5fid Faculty string 1fname Faculty string 2sal Faculty real 3


Relational Operations

We will consider how to implement:– Selection ( ) Selects a subset of rows from relation.– Projection ( ) Deletes unwanted columns from

relation.– Join ( ) Allows us to combine two relations.– Set-difference ( ) Tuples in reln. 1, but not in reln.

2.– Union ( ) Tuples in reln. 1 and in reln. 2.– Aggregation (SUM, MIN, etc.) and GROUP BY

Since each op returns a relation, ops can be composed! After we cover the operations, we will discuss how to optimize queries formed by composing them.


Schema for Examples

Similar to old schema; rname added for variations.

Reserves: Each tuple is 40 bytes long, 100 tuples per page,

1000 pages.

Sailors:Each tuple is 50 bytes long, 80 tuples per page,

500 pages.

Sailors (sid: integer, sname: string, rating: integer, age: real)

Reserves (sid: integer, bid: integer, day: dates, rname: string)


Three common techniques Indexing: If a selection or join condition is specified, use an

index to examine just the tuples that satisfy the condition.

Iteration: Examine all tuples in an input table, one after the other.( Some times we can examine index entries if the fields we are interested in are in index key ).

Partitioning: by partitioning tuples on a sort key, we can often decompose an operation into a less expensive collection of operations on partitions.

Sorting and Hashing are the common partitioning

techniques


Access PathAn access path as a way of retrieving tuples from a table andconsists of either (1) file scan o (2) An index plus a matching selection condition. Intuitively an index matches a selection condition if the indexcan be used to retrieve just the tuples that satisfy the condition. A hash index matches a CFN selection if there is a term attribute = value in selection condition for each attr. In the index’s search key A tree index matches a CNF selection if there is a term of theform attribute op value for each attr in a prefix of the index’s key.


Examples of Access PathsIf we have a hash index on search key <sname, bib, sid> thenwe can use the index to retrieve just the Seilors tuples with sname = ‘ Joy’ ^ bid = 5 ^ sid = 3 .

In contrast, if the index were a B+ tree it would matchsname = ‘ Joy’ ^ bid = 5 ^ sid = 3 and sname = ‘ Joy’ ^ bid = 5 However, it would not match bid = 5 ^ sid = 3 .

What if we have an index on the search key <bid, sid> and theselection codition is sname = ‘ Joy’ ^ bid = 5 ^ sid = 3 ?


Selectivity of Access Pths

The selectivity of an access path is the # of pages retrieved( indexpages + data pages) if we use the access path to retrieve all desiredtuples.The most selective access path is the one that retrieves the fewest

pages.The fraction of tuples in the table that satisfy the given conjunct iscalled reduction factor.Example: Suppose we have a hash index H on Sailors with search

key < sname, bid, sid> and we are given the selection coditionsname = ‘ Joy’ ^ bid = 5 ^ sid = 3 . The fraction of pages satisfyingthe primary conjunct is Npages(H)/NKeys(H).


Algorithm for Relational Operations (Selection)SELECT *FROM Reserves RWHERE R.rname < ‘C%’

The selection operator is simple retrieval of tuples from a table.For the selection of the form σR.attr op value (R) if there is indeson R.attr we have to scan RSize of result approximated as size of R * reduction factor; we will consider how to estimate reduction factors later.With no index, unsorted: Must essentially scan the whole relation;cost is M (#pages in R). With an index on selection attribute: Use index to find qualifying data entries, then retrieve corresponding data records. (Hash index useful only for equality selections.)


Using an Index for SelectionsCost depends on #qualifying tuples, and clustering.

– Cost of finding qualifying data entries (typically small) plus cost of retrieving records (could be large w/o clustering).

– In example, assuming uniform distribution of names, about 10% of tuples qualify (100 pages, 10000 tuples). With a clustered index, cost is little more than 100 I/Os; if unclustered, upto 10000 I/Os!

Important refinement for unclustered indexes: 1. Find qualifying data entries.2. Sort the rid’s of the data records to be retrieved.3. Fetch rids in order. This ensures that each data page is

looked at just once (though # of such pages likely to be higher than with clustering).


ProjectionIf duplications need not be eliminated , this can beaccomplished by simple iteration on either the table or anindex whose key is contains all necessary fields. If we have to eliminate the duplicates: let say we want to obtain < sid, bib> by projecting fro Reserves. We can first partition by scanning Reserves to obtain < sid, bid> pairs and than sort these pairs using < sid, bid

>as sort key. Sorting is very important operation in database systems.Sorting a table typically requires two or three passes, each

ofwhich reads and writes entire table.Projection can be optimized by combining with sorting.


Sort-based approach is the standard; If an index on the relation contains all wantedattributes in its search key, can do index-only

scan.– Apply projection techniques to data entries (much

smaller!)If an ordered (i.e., tree) index contains all wantedattributes as prefix of search key, can do even

better:– Retrieve data entries in order (index-only scan),

discard unwanted fields, compare adjacent tuples to check for duplicates.


JoinsJoins are expensive operations and very common.

Considerthe join of Reserves and Sailors with the Join condition R.sid = S.sid. Suppose that one of the tables, say Sailors has an index

onthe sid column. We can scan the Reserves and for each tuple , use the

indexto probe Sailors for matching tuple.( index nested loops

join)

If we don't have an index that matches the join codition oneither table, we cannot use index nested loops. In this

case,We can sort both tables on the joint column and then scan

them to find matches.( sort-merge join)


Join: Index Nested Loops

If there is an index on the join column of one relation (say S), can make it the inner and exploit the index.– Cost: M + ( (M*pR) * cost of finding matching S tuples)

For each R tuple, cost of probing S index is about 1.2 for hash index, 2-4 for B+ tree. Cost of then finding S tuples (assuming Alt. (2) or (3) for data entries) depends on clustering.– Clustered index: 1 I/O (typical), unclustered: upto 1

I/O per matching S tuple.

foreach tuple r in R doforeach tuple s in S where ri == sj do

add <r, s> to result


Examples of Index Nested Loops Hash-index (Alt. 2) on sid of Sailors (as inner):

– Scan Reserves: 1000 page I/Os, 100*1000 tuples.– For each Reserves tuple: 1.2 I/Os to get data

entry in index, plus 1 I/O to get (the exactly one) matching Sailors tuple. Total: 220,000 I/Os.

Hash-index (Alt. 2) on sid of Reserves (as inner):– Scan Sailors: 500 page I/Os, 80*500 tuples.– For each Sailors tuple: 1.2 I/Os to find index page

with data entries, plus cost of retrieving matching Reserves tuples. Assuming uniform distribution, 2.5 reservations per sailor (100,000 / 40,000). Cost of retrieving them is 1 or 2.5 I/Os depending on whether the index is clustered.


Join: Sort-Merge (R S)

Sort R and S on the join column, then scan them to do a ``merge’’ (on join col.), and output result tuples.– Advance scan of R until current R-tuple >= current S

tuple, then advance scan of S until current S-tuple >= current R tuple; do this until current R tuple = current S tuple.

– At this point, all R tuples with same value in Ri (current R group) and all S tuples with same value in Sj (current S group) match; output <r, s> for all pairs of such tuples.

– Then resume scanning R and S.R is scanned once; each S group is scanned once per

matching R tuple. (Multiple scans of an S group are likely to find needed pages in buffer.)

i=j


Example of Sort-Merge Join

Cost: M log M + N log N + (M+N)– The cost of scanning, M+N, could be M*N (very

unlikely!) With 35, 100 or 300 buffer pages, both Reserves and

Sailors can be sorted in 2 passes; total join cost: 7500.

sid sname rating age22 dustin 7 45.028 yuppy 9 35.031 lubber 8 55.544 guppy 5 35.058 rusty 10 35.0

sid bid day rname28 103 12/4/96 guppy28 103 11/3/96 yuppy31 101 10/10/96 dustin31 102 10/12/96 lubber31 101 10/11/96 lubber58 103 11/12/96 dustin


Other OperationsThe approach use to eliminate duplications for projectioncan be adapted for the set theoretic operations as union

andintersection. A SQL query contains also group –by andaggregation in addition to basic relational operations. Group-by is tupically implemented through sortingFor aggregate operations an additional effort is needed. ( Usage of main memory and counter variables while

tuples are retrieved ) Detaild explanations of all operator will come later ( Chapter 14)Next we will take look on query optimization.


Introduction to Query Optimization One of the most important tasks of RDBMS.Flexibility of relational query languges

allows towrite a query variety of ways and they

have different cost of execution. Queries are parsed and then presented to a

queryOptimizer, which is responsible for

identifying an efficient execution plan.


Schema for Examples

Similar to old schema; rname added for variations.

Reserves:– Each tuple is 40 bytes long, 100 tuples per

page, 1000 pages.Sailors:

– Each tuple is 50 bytes long, 80 tuples per page, 500 pages.

Sailors (sid: integer, sname: string, rating: integer, age: real)Reserves (sid: integer, bid: integer, day: dates, rname: string)


Motivating Example

Cost: 500+500*1000 I/OsBy no means the worst plan! Misses several opportunities:

selections could have been `pushed’ earlier, no use is made of any available indexes, etc.

Goal of optimization: To find more efficient plans that compute the same answer.

SELECT S.snameFROM Reserves R, Sailors SWHERE R.sid=S.sid AND R.bid=100 AND S.rating>5

Reserves Sailors

sid=sid

bid=100 rating > 5

sname

Reserves Sailors

sid=sid

bid=100 rating > 5

sname

(Simple Nested Loops)

(On-the-fly)

(On-the-fly)

RA Tree:

Plan:


Alternative Plans 1 (No Indexes)

Main difference: push selects. With 5 buffers, cost of plan:

– Scan Reserves (1000) + write temp T1 (10 pages, if we have 100 boats, uniform distribution).

– Scan Sailors (500) + write temp T2 (250 pages, if we have 10 ratings).– Sort T1 (2*2*10), sort T2 (2*3*250), merge (10+250)– Total: 3560 page I/Os.

If we used BNL join, join cost = 10+4*250, total cost = 2770. If we `push’ projections, T1 has only sid, T2 only sid and

sname:– T1 fits in 3 pages, cost of BNL drops to under 250 pages, total < 2000.

Reserves Sailors

sid=sid

bid=100

sname(On-the-fly)

rating > 5(Scan;write to temp T1)

(Scan;write totemp T2)

(Sort-Merge Join)


Alternative Plans 2With Indexes

With clustered index on bid of Reserves, we get 100,000/100 = 1000 tuples on 1000/100 = 10 pages.

INL with pipelining (outer is not materialized).

Decision not to push rating>5 before the join is based on availability of sid index on Sailors. Cost: Selection of Reserves tuples (10 I/Os); for each, must get matching Sailors tuple (1000*1.2); total 1210 I/Os.

Join column sid is a key for Sailors.–At most one matching tuple, unclustered index on sid OK.

–Projecting out unnecessary fields from outer doesn’t help.

Reserves

Sailors

sid=sid

bid=100

sname(On-the-fly)

rating > 5

(Use hashindex; donot writeresult to temp)

(Index Nested Loops,with pipelining )

(On-the-fly)


SummaryThere are several alternative evaluation algorithms

for each relational operator.A query is evaluated by converting it to a tree of

operators and evaluating the operators in the tree.

Must understand query optimization in order to fully understand the performance impact of a given database design (relations, indexes) on a workload (set of queries).

Two parts to optimizing a query:– Consider a set of alternative plans.

Must prune search space; typically, left-deep plans only.– Must estimate cost of each plan that is considered.

Must estimate size of result and cost for each plan node. Key issues: Statistics, indexes, operator implementations.


Homework

READING: Chapter 12 (DMS), 393- 419 pp

HOMEWORK: Answer the following questions from your textbook(DMS), page 170-171

Ex 12.1, 12.4Assigned 01/26/05 Due 02/03/05SUBMIT: hard copy by the beginning of class

Evaluation of Relational Operations

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