Download Chapter 13: Query Processing

Chapter 13: Query Processing
José Alferes
Versão modificada de Database System Concepts, 5th Ed.
©Silberschatz, Korth and Sudarshan
Chapter 13: Query Processing
 Overview of query processing and optimization
 Measures of Query Cost
 Selection Operation
 Sorting
 Join Operation
 Other Operations
 Evaluation of Expressions
 Intraquery Parallelism (in the book, at chapter 21)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.2
Basic Steps in Query Processing
1. Parsing and translation
2. Optimization
3. Evaluation
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.3
Parsing and Evaluation
 Parsing and translation

Translate the query into its internal form.

This is then translated into relational algebra.

(Extended) relational algebra is more compact, and differentiates
clearly among the various different operation

Parser checks syntax, verifies relations

This is a subject for compilers
 Evaluation

The query-execution engine takes a query-evaluation plan, executes
that plan, and returns the answers to the query.

The bulk of the problem lies in how to come up with good
evaluation plans!

This is “simply” executing a predefined plan (or program)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.4
Basic Steps in Query Processing :
Optimization
 A relational algebra expression may have many equivalent expressions

E.g., balance2500(balance(account)) is equivalent to
balance(balance2500(account))
 Each relational algebra operation can be evaluated using one of several
different algorithms

Correspondingly, a relational-algebra expression can be evaluated in
many ways.
 Annotated expression specifying detailed evaluation strategy is called an
evaluation-plan.

E.g., can use an index on balance to find accounts with balance < 2500,

or perform complete relation scan and discard accounts with balance 
2500
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.5
Basic Steps: Optimization (Cont.)
 Query Optimization: Amongst all equivalent evaluation plans choose
the one with lowest cost.

Cost is estimated using statistical information from the
database catalog
 e.g. number of tuples in each relation, size of tuples, etc.
 We start by showing
 Measure query costs (to have a measure on which to evaluate the
various algorithms and plans afterwards)

Algorithms for evaluating (main) relational algebra operations
 Combine algorithms for individual operations in order to evaluate a
complete expression
 How these algorithms and combinations can be parallelized, in
case parallel machines are available
 We continue then to study how to optimize queries

That is, how to find an evaluation plan with lowest estimated cost
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.6
Measures of Query Cost
 Cost is generally measured as total elapsed time for answering
query

Many factors contribute to time cost
 disk accesses, CPU, or even network communication
 Typically disk access is the predominant cost, and is also
relatively easy to estimate. Measured by taking into account
 Number of seeks
* average-seek-cost

Number of blocks read
* average-block-read-cost
 Number of blocks written
* average-block-write-cost
 The cost to write a block is greater than the cost to read
a block
– data is read back after being written to ensure that
the write was successful

The cost of a seek is usually much higher than that of a
block transfer read or write (one order of magnitude)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.7
Measures of Query Cost (Cont.)
 For simplicity we just use the number of block transfers from disk and the
number of seeks as the cost measures
 tT – time to transfer one block
 tS – time for one seek

Cost for b block transfers plus S seeks
b * t T + S * tS
 We do not include cost to writing output to disk in the cost formulae
 We ignore CPU costs for simplicity, as they tend to be much lower
 Real systems do take CPU cost into account, but they are clearly less
significant
 Evaluating the cost of an algorithm for query processing is similar to that in
“Algoritmos e Estruturas de Dados” but here the measures are quite
different.

The evaluation in terms of block transfers and seeks is substantially
different from that in term of number of steps
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.8
Selection Operation (recall)
 Notation:
 p(r)
 p is the selection predicate
 Defined by:
p(r) = {t | t  r and p(t)}
in which p is a formula of propositional calculus of terms
connected by:  (and),  (or),  (not)
Each term is of the form:
<attribute> op <attribute> or <constant>
where op can be one of: =, , >, . <. 
 Selection example:
 branch-name=‘Perryridge’ (account)
 For recalling other operators, see slides of “Bases de Dados 1”.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.9
Algorithms for Selection Operation
 File scan – search algorithms that locate and retrieve records that
fulfill a selection condition.
 Algorithm A1 (linear search). Scan each file block and test all records
to see whether they satisfy the selection condition.

Cost estimate = br block transfers + 1 seek
 br

If selection is on a key attribute, can stop on finding record


denotes number of blocks containing records from relation r
cost = (br /2) block transfers + 1 seek
This linear search can be always applied, regardless of:

selection condition or

ordering of records in the file, or

availability of indices
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.10
Algorithms for Selection (Cont.)
 A2 (binary search). Applicable only if the selection is an equality
comparison on the attribute on which file is ordered.

Assumes that the blocks of a relation are stored contiguously
 Cost estimate (number of disk blocks to be scanned):
 cost of locating the first tuple by a binary search on the
blocks
– log2(br) * (tT + tS)
If there are multiple records satisfying selection
– Add transfer cost of the number of blocks containing
records that satisfy selection condition
– Will see how to estimate this cost later
 If br is not too big, then most likely binary search doesn’t pay.

Note that tT is several (say, 50) times bigger than tS
 Estimates on the size of the relation are needed to wisely
choose which of the two algorithms is better for a specific
query at hands.

José Alferes - Adaptado de Database System Concepts - 5th Edition
13.11
Selections Using Indices
 Index scan – search algorithms that use an index

selection condition must be on search-key of index.
 A3 (primary index on candidate key, equality). Retrieve a single record
that satisfies the corresponding equality condition

Cost = (hi + 1) * (tT + tS)
where hi denotes the height of the index
 Recall that the height of a B+-tree index is logn/2(K), where n is the
number of index entries per node and K is the number of search keys.

E.g. for a relation r with 1.000.000 different search key, and with 100
index entries per node, hi = 4

Unless the relation is really small, this algorithms always “pays”
when indexes are available
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.12
Selections Using Indices (cont)
 A4 (primary index on nonkey, equality) Retrieve multiple records.

Records will be on consecutive blocks
 Let b = number of blocks containing matching records

Cost = hi * (tT + tS) + tS + tT * b
 A5 (equality on search-key of secondary index).
 Retrieve a single record if the search-key is a candidate key
 Cost = (hi + 1) * (tT + tS)
 Retrieve multiple records if search-key is not a candidate key
each of n matching records may be on a different block
 Cost = (hi + n) * (tT + tS)
– Can be very expensive if n is big!
» Note that it multiplies the time for seeks by n.

José Alferes - Adaptado de Database System Concepts - 5th Edition
13.13
Selections Involving Comparisons
 One can implement selections of the form AV (r) or A  V(r) by using

a linear file scan or binary search just as before,
 or by using indices in the following ways:
 A6 (primary index, comparison).
 For A  V(r) use index to find first tuple  v and scan relation
sequentially from there
 For AV (r) just scan relation sequentially till first tuple > v;
– Using the index would be useless, and would requires extra
seeks on the index file
 A7 (secondary index, comparison).
 For A  V(r) use index to find first index entry  v and scan index
sequentially from there, to find pointers to records.
 For AV (r) just scan leaf pages of index finding pointers to records,
till first entry > v
 In either case, retrieve records that are pointed to
– requires an I/O for each record (a lot!)
– Linear file scan may be much cheaper!!!!
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.14
Implementation of Complex Selections
 Conjunction: 1
2.
. . n(r)
 A8 (conjunctive selection using one index).
 Select a combination of i and algorithms A1 through A7 that
results in the least cost for i (r).

Test other conditions on tuple after fetching it into memory buffer.
 In this case the choice of the first condition is crucial!
 One must use estimates to know which one is better.
 A9 (conjunctive selection using multiple-key index).

Use appropriate composite (multiple-key) index if available.
 A10 (conjunctive selection by intersection of identifiers).
 Requires indices with record pointers.
 Use corresponding index for each condition, and take intersection
of all the obtained sets of record pointers.

Then fetch records from file
 If some conditions do not have appropriate indices, apply test in
memory.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.15
Algorithms for Complex Selections
 Disjunction:1
2 .
. . n (r).
 A11 (disjunctive selection by union of identifiers).

Applicable only if all conditions have available indices.

Otherwise use linear scan.

Use corresponding index for each condition, and take union of all the
obtained sets of record pointers.

Then fetch records from file
 Negation: (r)

Use linear scan on file

If very few records satisfy , and an index is applicable to 

Find satisfying records using index and fetch from file
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.16
Sorting
 Sorting algorithms are important in query processing at least for two
reasons:

The query itself may require sorting (order by clause)
 Some algorithms for other operations, like join, set operations and
aggregation, require that relation are previously sorted
 To sort a relation:

We may build an index on the relation, and then use the index to
read the relation in sorted order.
 This only sorts the relation logically, not physically
 May lead to one disk block access for each tuple.
 For relations that fit in memory sorting algorithms that you’ve
studied before, like quicksort, can be used.

For relations that don’t fit in memory special algorithms are
required, that take into account the measures in terms of disc
transfers and seeks.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.17
External Sort-Merge
 It is a sorting algorithm to be used when the whole relation does not
fit in memory.
Let M denote memory size (in pages).
1. Create sorted runs. Let i be 0 initially.
Repeatedly do the following till the end of the relation:
(a) Read M blocks of relation into memory
(b) Sort the in-memory blocks (with your favorite sorting algorithm)
(c) Write sorted data to run Ri; increment i.
Let the final value of i be N
2. Merge the runs (next slide)…..
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.18
External Sort-Merge (Cont.)
2. Merge the runs (N-way merge). We assume (for now) that N < M.
1.
Use N blocks of memory to buffer input runs, and 1 block to
buffer output. Read the first block of each run into its buffer
page
2.
repeat
3.
1.
Select the first record (in sort order) among all buffer
pages
2.
Write the record to the output buffer. If the output buffer is
full write it to disk.
3.
Delete the record from its input buffer page.
If the buffer page becomes empty then
read the next block (if any) of the run into the buffer.
until all input buffer pages are empty:
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.19
External Sort-Merge (Cont.)
 If N  M, several merge passes are required.

In each pass, contiguous groups of M - 1 runs are merged.

A pass reduces the number of runs by a factor of M -1, and
creates runs longer by the same factor.
 E.g.
If M=11, and there are 90 runs, one pass reduces
the number of runs to 9, each 10 times the size of the
initial runs

Repeated passes are performed till all runs have been
merged into one.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.20
Example: External Sorting Using Sort-Merge
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.21
External Merge Sort Transfer Cost
 Cost analysis:

Total number of merge passes required: logM–1(br/M).

Block transfers for initial run creation as well as in each
pass is 2br
 for
final pass, we don’t count write cost
– we ignore final write cost for all operations since the
output of an operation may be sent to the parent
operation without being written to disk
 Thus
total number of block transfers for external sorting:
br ( 2 logM–1(br / M) + 1)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.22
External Merge Sort Seek Cost
 Cost of seeks

During run generation: one seek to read each run and one seek to
write each run


2 br / M
During the merge phase

Buffer size: bb (read/write bb blocks at a time)

Need 2 br / bb seeks for each merge pass
– except the final one which does not require a write

Total number of seeks:
2 br / M + br / bb (2 logM–1(br / M) -1)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.23
Join Operation
 Several different algorithms to implement joins exist (not counting with
the ones involving parallelism)

Nested-loop join

Block nested-loop join

Indexed nested-loop join

Merge-join

Hash-join
 As for selection, the choice is based on cost estimate
 Examples in next slides use the following information

Number of records of customer: 10.000
depositor: 5.000

Number of blocks of customer:
depositor: 100
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.24
400
Nested-Loop Join
 The simplest join algorithms, that can be used independently of
everything (like the linear search for selection)
 To compute the theta join
r

s
for each tuple tr in r do begin
for each tuple ts in s do begin
test pair (tr,ts) to see if they satisfy the join condition 
if they do, add tr • ts to the result.
end
end
 r is called the outer relation and s the inner relation of the join.
 Quite expensive in general, since it requires to examine every pair of
tuples in the two relations.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.25
Nested-Loop Join (Cont.)
 In the worst case, if there is enough memory only to hold one block of
each relation, the estimated cost is
nr  bs + br
block transfers, plus
nr + br
seeks
 If the smaller relation fits entirely in memory, use that as the inner
relation.
 Reduces cost to br + bs block transfers and 2 seeks
 In general, it is much better to have the smaller relation as the outer
relation
 The number of block transfers is multiplied by the number of blocks
of the inner relation
 However, if the smaller relation is small enough to fit in memory, one
should use it as the inner relation!
 The choice of the inner and outer relation strongly depends on the
estimate of the size of each relation
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.26
Nested-Loop Join Cost in Example
 Assuming worst case memory availability cost estimate is


with depositor as outer relation:

5.000  400 + 100 = 2.000.100 block transfers,

5.000 + 100 = 5100 seeks
with customer as the outer relation

10.000  100 + 400 = 1.000.400 block transfers, 10.400 seeks
 If smaller relation (depositor) fits entirely in memory, the cost estimate
will be 500 block transfers and 2 seeks
 Instead of iterating over records, one could iterate over blocks. This way,
instead of nr  bs + br we would have br  bs + br block transfers
 This is the basis of the block nested-loops algorithm (next slide).
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.27
Block Nested-Loop Join
 Variant of nested-loop join in which every block of inner relation is
paired with every block of outer relation.
for each block Br of r do begin
for each block Bs of s do begin
for each tuple tr in Br do begin
for each tuple ts in Bs do begin
Check if (tr,ts) satisfy the join condition
if they do, add tr • ts to the result.
end
end
end
end
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.28
Block Nested-Loop Join Cost
 Worst case estimate: br  bs + br block transfers and 2 * br seeks

Each block in the inner relation s is read once for each block in
the outer relation (instead of once for each tuple in the outer
relation
 Best case (when smaller relation fits into memory): br + bs block
transfers plus 2 seeks.
 Some improvements to nested loop and block nested loop algorithms
can be made:

Scan inner loop forward and backward alternately, to make use of
the blocks remaining in buffer (with LRU replacement)

Use index on inner relation if available to faster get the tuples
which match the tuple of the outer relation at hands
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.29
Indexed Nested-Loop Join
 Index lookups can replace file scans if

join is an equi-join or natural join and

an index is available on the inner relation’s join attribute

In some cases, it pays to construct an index just to compute a join.
 For each tuple tr in the outer relation r, use the index on s to look up
tuples in s that satisfy the join condition with tuple tr.
 Worst case: buffer has space for only one page of r, and, for each tuple
in r, we perform an index lookup on s.
 Cost of the join: br (tT + tS) + nr  c

Where c is the cost of traversing index and fetching all matching s
tuples for one tuple or r

c can be estimated as cost of a single selection on s using the join
condition (usually quite low, when compared to the join)
 If indices are available on join attributes of both r and s,
use the relation with fewer tuples as the outer relation.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.30
Example of Nested-Loop Join Costs
 Compute depositor




customer, with depositor as the outer relation.
Let customer have a primary B+-tree index on the join attribute
customer-name, which contains 20 entries in each index node.
Since customer has 10.000 tuples, the height of the tree is 4, and one
more access is needed to find the actual data
depositor has 5.000 tuples
For nested loop: 2.000.100 block transfers and 5.100 seeks
 Cost of block nested loops join


400*100 + 100 = 40.100 block transfers + 2 * 100 = 200 seeks
Cost of indexed nested loops join

100 + 5.000 * 5 = 25.100 block transfers and seeks.

CPU cost likely to be less than that for block nested loops join

However in terms of time for transfers and seeks, in this case
using the index doesn’t pay (this is specially so because the
relations are small)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.31
Merge-Join
1.
Sort both relations on their join attribute (if not already sorted on the join
attributes).
2.
Merge the sorted relations to join them
1.
Join step is similar to the merge stage of the sort-merge algorithm.
2.
Main difference is handling of duplicate values in join attribute — every
pair with same value on join attribute must be matched
3.
Detailed algorithm may be found in the book
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.32
Merge-Join (Cont.)
 Can be used only for equi-joins and natural joins
 Each block needs to be read only once (assuming that all tuples for any
given value of the join attributes fit in memory)
 Thus the cost of merge join is (where bb is the number of blocks in
allocated in memory):
br + bs block transfers + br / bb + bs / bb seeks

+ the cost of sorting if relations are unsorted.
 hybrid merge-join: If one relation is sorted, and the other has a
secondary B+-tree index on the join attribute

Merge the sorted relation with the leaf entries of the B+-tree .

Sort the result on the addresses of the unsorted relation’s tuples

Scan the unsorted relation in physical address order and merge with
previous result, to replace addresses by the actual tuples

Sequential scan more efficient than random lookup
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.33
Hash-Join
 Also only applicable for equi-joins and natural joins.
 A hash function h is used to partition tuples of both relations
 h maps JoinAttrs values to {0, 1, ..., n}, where JoinAttrs denotes the
common attributes of r and s used in the natural join.
 r0, r1, . . ., rn denote partitions of r tuples
 Each tuple tr  r is put in partition ri where i = h(tr [JoinAttrs]).
 s0, s1. . ., sn denotes partitions of s tuples
Each tuple ts s is put in partition si, where i = h(ts [JoinAttrs]).
 General idea:
 Partition the relations according to this
 Then perform the join on each partition ri and si


There is no need to compute the join between different
partitions since an r tuple and an s tuple that satisfy the join
condition will have the same value for the join attributes. If that
value is hashed to some value i, the r tuple has to be in ri and
the s tuple in si.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.34
Hash-Join (Cont.)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.35
Hash-Join Algorithm
The hash-join of r and s is computed as follows.
1. Partition the relation s using hashing function h. When partitioning a
relation, one block of memory is reserved as the output buffer for
each partition.
2. Partition r similarly.
3. For each i:
(a) Load si into memory and build an in-memory hash index on it
using the join attribute. This hash index uses a different hash
function than the earlier one h.
(b) Read the tuples in ri from the disk one by one. For each tuple
tr locate each matching tuple ts in si using the in-memory hash
index. Output the concatenation of their attributes.
Relation s is called the build input and
r is called the probe input.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.36
Hash-Join algorithm (Cont.)
 The number of partitions n for the hash function h is chosen such that
each si should fit in memory.
Typically n is chosen as bs/M * f where f is a “fudge factor”,
typically around 1.2, to avoid overflows
 The probe relation partitions ri need not fit in memory
 Recursive partitioning required if number of partitions n is greater
than number of pages M of memory.

instead of partitioning n ways, use M – 1 partitions for s
 Further partition the M – 1 partitions using a different hash
function
 Use same partitioning method on r
 Rarely required: e.g., recursive partitioning not needed for
relations of 1GB or less with memory size of 2MB, with block size
of 4KB.


So is not further considered here (see the book for details on
the associated costs)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.37
Cost of Hash-Join
 The cost of hash join is
3(br + bs) +4  nh block transfers +
2( br / bb + bs / bb) seeks
 If the entire build input can be kept in main memory no partitioning is
required
 Cost estimate goes down to br + bs.
 For the running example, assume that memory size is 20 blocks
 bdepositor= 100 and bcustomer = 400.
 depositor is to be used as build input. Partition it into five partitions,
each of size 20 blocks. This partitioning can be done in one pass.
 Similarly, partition customer into five partitions, each of size 80. This is
also done in one pass.
 Therefore total cost, ignoring cost of writing partially filled blocks:

3(100 + 400) = 1.500 block transfers +
2( 100/3 + 400/3) = 336 seeks
 The best we had up to here was 40.100 block transfers plus 200 seeks
(for block nested loop) or 25,100 block transfers and seeks (for index
nested loop)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.38
Complex Joins
 Join with a conjunctive condition:
r
1  2...   n
s

Either use nested loops/block nested loops, or

Compute the result of one of the simpler joins r

i
s
final result comprises those tuples in the intermediate result
that satisfy the remaining conditions
1  . . .  i –1  i +1  . . .  n
 Join with a disjunctive condition
r
1  2 ...  n s

Either use nested loops/block nested loops, or

Compute as the union of the records in individual joins r
(r
1 s)
 (r
2
s)  . . .  (r
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.39
n
s)
 i s:
Other Operations
 Duplicate elimination can be implemented via hashing or sorting.

On sorting duplicates will come adjacent to each other, and all but
one set of duplicates can be deleted.

Optimization: duplicates can be deleted during run generation as
well as at intermediate merge steps in external sort-merge.

Hashing is similar – duplicates will come into the same bucket.
 Projection:

perform projection on each tuple

followed by duplicate elimination.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.40
Other Operations : Aggregation
 Aggregation can be implemented in similarly to duplicate elimination.

Sorting or hashing can be used to bring tuples in the same group
together, and then the aggregate functions can be applied on each
group.

Optimization: combine tuples in the same group during run
generation and intermediate merges, by computing partial
aggregate values

For count, min, max, sum: keep aggregate values on tuples
found so far in the group.
– When combining partial aggregate for count, add up the
aggregates

For avg, keep sum and count, and divide sum by count at the
end
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13.41
Other Operations : Set Operations


Set operations (,  and ): can either use variant of merge-join after
sorting, or variant of hash-join.
E.g., Set operations using hashing:
1. Partition both relations using the same hash function
2. Process each partition i as follows.
1. Using a different hashing function, build an in-memory hash index
on ri.
2. Process si as follows
 r  s:
1. Add tuples in si to the hash index if they are not already in it.
2. At end of si add the tuples in the hash index to the result.
 r  s:
1. output tuples in si to the result if they are already there in the
hash index
 r – s:
1. for each tuple in si, if it is there in the hash index, delete it
from the index.
2.
At end of si add remaining tuples in the hash index to the
result.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.42
Other Operations : Outer Join
 Outer join can be computed either as

A join followed by addition of null-padded non-participating tuples.

by modifying the join algorithms.
 Modifying merge join to compute r
s
s, non participating tuples are those in r – R(r

In r

Modify merge-join to compute r
s: During merging, for every
tuple tr from r that do not match any tuple in s, output tr padded with
nulls.

Right outer-join and full outer-join can be computed similarly.
 Modifying hash join to compute r
s)
s

If r is probe relation, output non-matching r tuples added with nulls

If r is build relation, when probing keep track of which
r tuples matched s tuples. At end of si output
non-matched r tuples padded with nulls
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.43
Evaluation of Expressions
 So far we have seen algorithms for individual operations

These have then to be combined to evaluate complex
expressions, with several operations
 Alternatives for evaluating an entire expression tree

Materialization: generate results of an expression whose inputs
are relations or are already computed, materialize (store) it on
disk. Repeat.

Pipelining: pass on tuples to parent operations even as an
operation is being executed
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.44
Materialization
 Materialized evaluation: evaluate one operation at a time,
starting at the lowest-level. Use intermediate results
materialized into temporary relations to evaluate next-level
operations.
 E.g., in figure below, compute and store
 balance2500 (account )
then compute the store its join with customer, and finally
compute the projections on customer-name.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.45
Materialization (Cont.)
 Materialized evaluation is always applicable
 It may require considerable storage space. Moreover, cost of writing
results to disk and reading them back can be quite high

Our cost formulas for operations ignore cost of writing results to
disk, so

Overall cost = Sum of costs of individual operations +
cost of writing intermediate results to disk
 Double buffering: use two output buffers for each operation, when one
is full, write it to disk while the other is getting filled

Allows overlap of disk writes with computation and reduces
execution time
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.46
Pipelining
 Pipelined evaluation : evaluate several operations simultaneously,
passing the results of one operation on to the next.
 E.g., in previous expression tree, don’t store result of
 balance 2500 (account )


instead, pass tuples directly to the join.
Similarly, don’t store result of join, pass tuples directly to projection.
 It is much cheaper than materialization: there is no need to store a
temporary relation to disk.
 Pipelining may not always be possible – e.g., sort and hash-join where a
preliminary phase is required over the whole relations
 For pipelining to be effective, use evaluation algorithms that generate
output tuples even as tuples are received for inputs to the operation.
 Pipelines can be executed in two ways: demand driven and producer
driven
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13.47
Pipelining (Cont.)
 In producer-driven (or eager or push) pipelining


Operators produce tuples eagerly and pass them up to their parents

Buffer maintained between operators, child puts tuples in buffer,
parent removes tuples from buffer

if buffer is full, child waits till there is space in the buffer, and then
generates more tuples
System schedules operations that have space in output buffer and
can process more input tuples
 In demand driven (or lazy, or pull) evaluation

system repeatedly requests next tuple from top level operation

Each operation requests next tuple from children operations as
required, in order to output its next tuple

In between calls, operation has to maintain “state” so it knows what
to return next
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.48
Pipelining (Cont.)
 Implementation of pull pipelining

Each operation is implemented as an iterator implementing the
following operations
 open()
– E.g. file scan: initialize file scan
» state: pointer to beginning of file
– E.g.merge join: sort relations;
» state: pointers to beginning of sorted relations
 next()
– E.g. for file scan: Output next tuple, and advance and store
file pointer
– E.g. for merge join: continue with merge from earlier state
till
next output tuple is found. Save pointers as iterator state.
 close()
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.49
Evaluation Algorithms for Pipelining
 Some algorithms are not able to output results even as they get input
tuples

E.g. merge join, or hash join

intermediate results written to disk and then read back
 Algorithm variants to generate (at least some) results on the fly, as input
tuples are read in

E.g. hybrid hash join (see book for details) generates output tuples
even as probe relation tuples in the in-memory partition (partition 0)
are read in
 It is clear that pipelining could greatly benefit from parallel processing,
especially of sufficiently independent sub-expressions

And this is not the only chance for parallelism in query processing!
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13.50
Intraquery Parallelism
 Execution of a single query in parallel on multiple processors/disks;
important for speeding up long-running queries, in case machines with
several processors are available.
 Two complementary forms of intraquery parallelism :

Intraoperation Parallelism – parallelize the execution of each
individual operation in the query.

Interoperation Parallelism – execute the different operations in a
query expression in parallel (as for pipelining)
 Intraoperation parallelism has the potential for better improvements with
increasing parallelism because the number of tuples processed by each
operation is typically more than the number of operations in a query
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13.51
Interoperator Parallelism
 Pipelined parallelism

Consider a join of four relations
 r1


r2
r3
r4
Set up a pipeline that computes the three joins in parallel

Let P1 be assigned the computation of
temp1 = r1 r2

P2 be assigned the computation of temp2 = temp1

and P3 be assigned the computation of temp2
r3
r4
Each of these operations can execute in parallel, sending result
tuples it computes to the next operation even as it is computing
further results

Provided a pipelineable join evaluation algorithm (e.g. indexed
nested loops join) is used
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.52
Factors Limiting Utility of Pipeline
Parallelism
 Pipeline parallelism is useful since it avoids writing intermediate results to
disk
 Useful with small number of processors, but does not scale up well with
more processors. One reason is that pipeline chains do not attain
sufficient length.
 Cannot pipeline operators which do not produce output until all inputs
have been accessed (e.g. aggregate and sort)
 Little speedup is obtained for the frequent cases of skew in which
one operator's execution cost is much higher than the others.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.53
Independent Parallelism
 Independent parallelism

Consider a join of four relations
r1 r2
r3
r4
Let P1 be assigned the computation of
temp1 = r1
r2
 And P2 be assigned the computation of temp2 = r3
r4
 And P3 be assigned the computation of temp1
temp2
 P1 and P2 can work independently in parallel

P3 has to wait for input from P1 and P2
– Can pipeline output of P1 and P2 to P3, combining
independent parallelism and pipelined parallelism
 Does not provide a high degree of parallelism
 useful with a lower degree of parallelism.


less useful in a highly parallel system,
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13.54
Parallel Processing of Relational Operations
 Our discussion of parallel algorithms assumes:

shared-nothing architecture (i.e. no shared memory or disk)

n processors, P0, ..., Pn-1, and n disks D0, ..., Dn-1, where disk Di is
associated with processor Pi.
 If a processor has multiple disks they can simply simulate a single disk
Di.
 Shared-nothing architectures can be efficiently simulated on shared-
memory and shared-disk systems.

Algorithms for shared-nothing systems can thus be run on sharedmemory and shared-disk systems.

However, some optimizations may be possible.
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13.55
Parallel Sort
Range-Partitioning Sort
 Choose processors P0, ..., Pm, where m  n -1 to do sorting.
 Create range-partition vector with m entries, on the sorting attributes
 Redistribute the relation using range partitioning

all tuples that lie in the ith range are sent to processor Pi

Pi stores the tuples it received temporarily on disk Di.

This step requires I/O and communication overhead.
 Each processor Pi sorts its partition of the relation locally.
 Each processors executes same operation (sort) in parallel with other
processors, without any interaction with the others (data parallelism).
 Final merge operation is trivial: range-partitioning ensures that, for i  j,
the key values in processor Pi are all less than the key values in Pj.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.56
Parallel Sort (Cont.)
Parallel External Sort-Merge
 Assume the relation has already been partitioned among disks D0, ...,
Dn-1 (in whatever manner).
 Each processor Pi locally sorts the data on disk Di.
 The sorted runs on each processor are then merged to get the final
sorted output.
 Parallelize the merging of sorted runs as follows:

The sorted partitions at each processor Pi are range-partitioned
across the processors P0, ..., Pm-1.

Each processor Pi performs a merge on the streams as they are
received, to get a single sorted run.

The sorted runs on processors P0,..., Pm-1 are concatenated to get
the final result.
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13.57
Parallel Join – General Idea
 Parallel join algorithms attempt to split the pairs to be tested (each
with an element from each of the relation to join) over several
processors. Each processor then computes part of the join locally.
 In a final step, the results from each processor can be collected
together to produce the final result.
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13.58
Partitioned Join
 For equi-joins and natural joins, it is possible to partition the two input
relations across the processors, and compute the join locally at each
processor.
 Let r and s be the input relations, and we want to compute r
r.A=s.B
s.
 r and s each are partitioned into n partitions, denoted r0, r1, ..., rn-1 and s0,
s1, ..., sn-1.
 Can use either range partitioning or hash partitioning.
 r and s must be partitioned on their join attributes r.A and s.B), using the
same range-partitioning vector or hash function.
 Partitions ri and si are sent to processor Pi,
 Each processor Pi locally computes ri
join methods can be used.
ri.A=si.B si. Any of the standard
 This can be further elaborated to account for partitioning hash join (see
book for details)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.59
Partitioned Join (Cont.)
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.60
Fragment-and-Replicate Join
 It is used when the relations cannot be partitioned.

Note that partitioning is not always possible
 e.g., for non-equijoin conditions, such as r.A > s.B.
 General idea:
 Fragment r into n relations, and s into m relations
 Use n*m processors to compute joins between all partitions
 This requires replicating the fragments
 Make the union of the obtained joins
 Special case – asymmetric fragment-and-replicate:



One of the relations, say r, is partitioned; any partitioning
technique can be used.
The other relation, s, is replicated across all the processors.
Processor Pi then locally computes the join of ri with all of s using
any join technique.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.61
Depiction of Fragment-and-Replicate Joins
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.62
Fragment-and-Replicate Join (Cont.)
 General case: reduces the sizes of the relations at each processor.

r is partitioned into n partitions,r0, r1, ..., r n-1;s is partitioned into m
partitions, s0, s1, ..., sm-1.

Any partitioning technique may be used.

There must be at least m * n processors.

Label the processors as


P0,0, P0,1, ..., P0,m-1, P1,0, ..., Pn-1m-1.

Pi,j computes the join of ri with sj. In order to do so, ri is
replicated to Pi,0, Pi,1, ..., Pi,m-1, while si is replicated to P0,i, P1,i,
..., Pn-1,i
Any join technique can be used at each processor Pi,j.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.63
Fragment-and-Replicate Join (Cont.)
 Both versions of fragment-and-replicate work with any join condition, since
every tuple in r can be tested with every tuple in s.
 Usually has a higher cost than partitioning, since one of the relations (for
asymmetric fragment-and-replicate) or both relations (for general fragmentand-replicate) have to be replicated.
 Sometimes asymmetric fragment-and-replicate is preferable even though
partitioning could be used.

E.g., say s is small and r is large, and already partitioned. It may be
cheaper to replicate s across all processors, rather than repartition r
and s on the join attributes.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.64
Parallel Nested-Loop Join
 Assume that

relation s is much smaller than relation r and that r is stored by
partitioning.

there is an index on a join attribute of relation r at each of the
partitions of relation r.
 Use asymmetric fragment-and-replicate, with relation s being
replicated, and using the existing partitioning of relation r.
 Each processor Pj where a partition of relation s is stored reads the
tuples of relation s stored in Dj, and replicates the tuples to every other
processor Pi.

At the end of this phase, relation s is replicated at all sites that
store tuples of relation r.
 Each processor Pi performs an indexed nested-loop join of relation s
with the ith partition of relation r.
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13.65
Parallel Selection
Selection (r)
 If  is of the form ai = v, where ai is an attribute and v a value.

If r is partitioned on ai the selection is performed at a single
processor.
 If  is of the form l  ai  u (i.e.,  is a range selection) and the relation
has been range-partitioned on ai

Selection is performed at each processor whose partition overlaps
with the specified range of values.
 In all other cases: the selection is performed in parallel at all the
processors.
José Alferes - Adaptado de Database System Concepts - 5th Edition
13.66
Other Relational Operations
 Duplicate elimination

Perform by using either of the parallel sort techniques


eliminate duplicates as soon as they are found during sorting.
Can also partition the tuples (using either range- or hashpartitioning) and perform duplicate elimination locally at each
processor.
 Projection

Projection without duplicate elimination can be performed as
tuples are read in from disk in parallel.

If duplicate elimination is required, any of the above duplicate
elimination techniques can be used.
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13.67
Grouping/Aggregation
 Partition the relation on the grouping attributes and then compute the
aggregate values locally at each processor.
 Can reduce cost of transferring tuples during partitioning by partly
computing aggregate values before partitioning.
 Consider the sum aggregation operation:

Perform aggregation operation at each processor Pi on those
tuples stored on disk Di


results in tuples with partial sums at each processor.
Result of the local aggregation is partitioned on the grouping
attributes, and the aggregation performed again at each processor
Pi to get the final result.
 Fewer tuples need to be sent to other processors during partitioning.
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13.68
Cost of Parallel Evaluation of Operations
 If there is no skew in the partitioning, and there is no overhead due to
the parallel evaluation, expected speed-up will be 1/n
 If skew and overheads are also to be taken into account, the time
taken by a parallel operation can be estimated as
Tpart + Tasm + max (T0, T1, …, Tn-1)

Tpart is the time for partitioning the relations

Tasm is the time for assembling the results

Ti is the time taken for the operation at processor Pi

this needs to be estimated taking into account the skew, and
the time wasted in contentions.
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13.69
Query processing in Oracle
 Oracle implements most of the algorithms we’ve seen for query
processing of the various operations


For selection

Full table scan (i.e. linear search algorithm)

Index scan (as described above in these slides)

Index fast full scan (transverse the whole table using the B+
index)

Cluster and hash cluster access (access data by using cluster
key)
For join

(Block) nested loop join (possibly using indexes, when
available)

Sort-merge join

Hash join
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13.70
Query processing in Oracle (Cont.)
 The choice of the algorithm to be used in each operation is done by
the query optimizer (we will see more on this afterwards)
 However, the user can force specific algorithms by providing hints
when writing the query:
select /*+ here_comes_the_hint */ …
 Quite a few hints can be added. Here we name just a few.

Hints for forcing a specific algorithm (or index file) to be used in a
selection
 Hints for ordering the relations in a join (i.e. to choose the outer
and the inner relations, or probe and build relations)

Hints for choosing an algorithm for join, and possibly an index file
if appropriate;
 Hints for forcing parallelism; Hints for guiding the optimizer
 …
 See more at the reference manual, in chapter 2 (Basic Elements
of Oracle SQL) under the section on “Comments”
 It may seem a strange place to have it, but there is where it is!
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Some query hints in Oracle
 full(table_name)

Instructs the processor to use a full table scan
 index(table_name index_name)

The processor uses index_name to scan the table
 no_index(table_name index_name)

Forbids the use index_name to scan the table
 index_combine(table_name index_names)

Builds a bitmap for the index files specified, and uses it in the scan
of the table
 ordered

Instructs the processor to use the relations in a join in the exact
order they appear in the select query
 star_transformation

The order chosen for join has the smaller relations first
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13.72
Some (more) query hints in Oracle
 use_nl(table_name table_name)

Uses (block) nested loop for the join between the tables
 use_nl_with_index(table_name index_name)
 The table is to be used as the inner relation of the join, in a nested
loop algorithm, using the index file in the inner loop
 use_merge(table_name table_name)

Uses sort-merge algorithm for the join between the tables
 use_hash(table_name table_name)

Uses hash join algorithm for the join between the tables
 first_rows(n)

Instructs the processor to use the fastest plan for providing the
first n tuple of the result (as in pipelining)
 all_rows

The optimization is made assuming taking into account the cost of
obtaining all the tuples of the result
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13.73
Parallel query processing in Oracle




Oracle allows for parallelism in query processing, whenever multiple
processors are available:
alter session enable parallel query [parallel_max servers n]
This enable the use of parallel algorithms for intraoperation and for parallelism
in pipelining, using n processors
 Other options are available for specifying parallelism groups, number of
threads per cpu, etc.
 Pipelining can be explicitly enforced by using pipelined PL/SQL table
functions
Parallelism can be specified to be used in all algorithms depending on a
specific table with
alter table table_name parallel
There are also hints for driving into parallelism:
 parallel(table_name, n)
 Use n processors in partitioning parallel algorithms involving
table_name in the query where the hint is given
 If default is given instead of n then the default value for the session is
used
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13.74