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Chapter 17: Parallel Databases
· Introduction
· I/O Parallelism
· Interquery Parallelism
· Intraquery Parallelism
· Intraoperation Parallelism
· Interoperation Parallelism
· Design of Parallel Systems
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Introduction
· Parallel machines are becoming quite common and affordable
­ Prices of microprocessors, memory and disks have
dropped sharply
· Databases are growing increasingly large
­ large volumes of transaction data are collected and stored
for later analysis.
­ multimedia objects like images are increasingly stored in
databases
· Large-scale parallel database systems increasingly used for:
­ processing time-consuming decision-support queries
­ providing high throughput for transaction processing
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Parallelism in Databases
· Data can be partitioned across multiple disks for parallel I/O.
· Individual relational operations (e.g., sort, join, aggregation)
can be executed in parallel
­ data can be partitioned and each processor can work
independently on its own partition.
· Queries are expressed in high level language (SQL, translated
to relational algebra)
­ makes parallelization easier.
· Different queries can be run in parallel with each other.
Concurrency control takes care of conflicts.
· Thus, databases naturally lend themselves to parallelism.
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I/O Parallelism
· Reduce the time required to retrieve relations from disk by
partitioning the relations on multiple disks.
· Horizontal partitioning ­ tuples of a relation are divided among
many disks such that each tuple resides on one disk.
· Partitioning techniques (number of disks = n):
Round-robin :
Send the ith tuple inserted in the relation to disk i mod n.
Hash partitioning :
­ Choose one or more attributes as the partitioning
attributes.
­ Choose hash function h with range 0 . . . n - 1.
­ Let i denote result of hash function h applied to the
partitioning attribute value of a tuple. Send tuple to disk i.
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I/O Parallelism (Cont.)
· Partitioning techniques (cont.):
Range partitioning :
­ Choose an attribute as the partitioning attribute.
­ A partitioning vector [v0, v1, . . . , vn-2] is chosen
­ Let v be the partitioning attribute value of a tuple. Tuples
such that vi  v < vi+1 go to disk i + 1. Tuples with v < v0
go to disk 0 and tuples with v  vn-2 go to disk n - 1.
E.g., with a partitioning vector [5,11], a tuple with
partitioning attribute value of 2 will go to disk 0, a tuple with
value 8 will go to disk 1, while a tuple with value 20 will go
to disk 2.
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Comparison of Partitioning Techniques
· Evaluate how well partitioning techniques support the following
types of data access:
1. Scanning the entire relation.
2. Locating a tuple associatively ­ point queries.
­ E.g., r.A = 25.
3. Locating all tuples such that the value of a given attribute
lies within a specified range ­ range queries.
­ E.g., 10  r.A < 25.
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Comparison of Partitioning Techniques (Cont.)
· Round-robin.
­ Best suited for sequential scan of entire relation on each
query.
 All disks have almost an equal number of tuples; retrieval
work is thus well balanced between disks.
­ Range queries are difficult to process
 No clustering ­ tuples are scattered across all disks
Database Systems Concepts 17.7 Silberschatz, Korth and Sudarshan c 1997
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Comparison of Partitioning Techniques (Cont.)
· Hash partitioning.
­ Good for sequential access
 Assuming hash function is good, and partitioning
attributes form a key, tuples will be equally distributed
between disks
 Retrieval work is then well balanced between disks.
­ Good for point queries on partitioning attribute
 Can lookup single disk, leaving others available for
answering other queries.
 Index on partitioning attribute can be local to disk, making
lookup and update more efficient
­ No clustering, so difficult to answer range queries
Database Systems Concepts 17.8 Silberschatz, Korth and Sudarshan c 1997
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Comparison of Partitioning Techniques (Cont.)
· Range partitioning.
­ Provides data clustering by partitioning attribute value.
­ Good for sequential access
­ Good for point queries on partitioning attribute: only one
disk needs to be accessed.
­ For range queries on partitioning attribute, one to a few
disks may need to be accessed
 Remaining disks are available for other queries.
 Good if result tuples are from one to a few blocks.
 If many blocks are to be fetched, they are still fetched
from one to a few disks, and potential parallelism in disk
access is wasted
 Example of execution skew.
Database Systems Concepts 17.9 Silberschatz, Korth and Sudarshan c 1997
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Partitioning a Relation across Disks
· If a relation contains only a few tuples which will fit into a single
disk block, then assign the relation to a single disk.
· Large relations are preferably partitioned across all the
available disks.
· If a relation consists of m disk blocks and there are n disks
available in the system, then the relation should be allocated
min(m, n) disks.
Database Systems Concepts 17.10 Silberschatz, Korth and Sudarshan c 1997
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Handling of Skew
· The distribution of tuples to disks may be skewed -- i.e., some
disks have many tuples, while others may have fewer tuples.
· Types of skew:
­ Attribute-value skew.
 Some values appear in the partitioning attributes of many
tuples; all the tuples with the same value for the
partitioning attribute end up in the same partition.
 Can occur with range-partitioning and hash-partitioning.
­ Partition skew.
 With range-partitioning, badly chosen partition vector
may assign too many tuples to some partitions and too
few to others.
 Less likely with hash-partitioning if a good hash-function
is chosen.
Database Systems Concepts 17.11 Silberschatz, Korth and Sudarshan c 1997
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Handling Skew in Range-Partitioning
· To create a balanced partitioning vector (assuming partitioning
attribute forms a key of the relation):
­ Sort the relation on the partitioning attribute.
­ Construct the partition vector by scanning the relation in
sorted order as follows.
 After every 1/nth
of the relation has been read, the value
of the partitioning attribute of the next tuple is added to
the partition vector.
· Alternative technique based on histograms used in practice
(will see later).
Database Systems Concepts 17.12 Silberschatz, Korth and Sudarshan c 1997
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Interquery Parallelism
· Queries/transactions execute in parallel with one another.
· Increases transaction throughput; used primarily to scale up a
transaction processing system to support a larger number of
transactions per second.
· Easiest form of parallelism to support, particularly in a
shared-memory parallel database, because even sequential
database systems support concurrent processing.
· More complicated to implement on shared-disk or
shared-nothing architectures
­ Locking and logging must be coordinated by passing
messages between processors.
­ Data in a local buffer may have been updated at another
processor.
­ Cache-coherency has to be maintained -- reads and writes
of data in buffer must find latest version of data.
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Cache Coherency Protocol
· Example of a cache coherency protocol for shared disk
systems:
­ Before reading/writing to a page, the page must be locked
in shared/exclusive mode.
­ On locking a page, the page must be read from disk
­ Before unlocking a page, the page must be written to disk if
it was modified.
· More complex protocols with fewer disk reads/writes exist.
· Cache coherency protocols for shared-nothing systems are
similar. Each database page is assigned a home processor.
Requests to fetch the page or write it to disk are sent to the
home processor.
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Intraquery Parallelism
· Execution of a single query in parallel on multiple
processors/disks; important for speeding up long-running
queries.
· 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.
the first form scales better 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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Parallel Processing of Relational Operations
· Our discussion of parallel algorithms assumes:
­ read-only queries
­ shared-nothing architecture
­ n processors, P0, . . . , Pn-1, and n disks D0, . . . , Dn-1,
where disk Di is associated with processor Pi.
· Shared-nothing architectures can be efficiently simulated on
shared-memory and shared-disk systems.
­ Algorithms for shared-nothing systems can thus be run on
shared-memory and shared-disk systems.
­ However, some optimizations may be possible.
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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 .
· 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 1  i < j  m, the key values in processor Pi are all less
than the key values in Pj .
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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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Parallel Join
· The join operation requires pairs of tuples to be tested to see if
they satisfy the join condition, and if they do, the pair is added
to the join output.
· Parallel join algorithms attempt to split the pairs to be tested
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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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 1r.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 1ri .A=si .B si . Any of the
standard join methods can be used.
Database Systems Concepts 17.20 Silberschatz, Korth and Sudarshan c 1997
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Partitioned Join (Cont.)
P0r0
P1r1
sr
P2r2
P3r3
s0
s1
s2
s3
...
...
...
.
.
.
.
.
.
.
.
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Fragment-and-Replicate Join
· Partitioning not possible for some join conditions
­ e.g., non-equijoin conditions, such as r.A > s.B.
· For joins were partitioning is not applicable, parallelization can
be accomplished by fragment and replicate technique.
· 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.
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Depiction of Fragment-and-Replicate Joins
r0 P0,0
s0 s1 s2
s
s3 sm­1
r1
r r2
r3
rn­1 Pn­1,m­1
.
.
.
P0r0
P1r1
r s
P2r2
P3r3
.
..
.
..
P1,0
P2,0
P0,1
P1,1
P2,1
P0,2
P1,2
P0,3
. . .
. . . . .
.
.
.
.
.
(a) Asymmetric
fragment and replicate
(b) Fragment and replicate
Database Systems Concepts 17.23 Silberschatz, Korth and Sudarshan c 1997
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Fragment-and-Replicate Join (Cont.)
· General case: reduces the sizes of the relations at each
processor.
­ r is partitioned into n partitions, r0, r1, . . . , rn-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-1,m-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.
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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 fragment-and-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.
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Partitioned Parallel Hash-Join
Also assume s is smaller than r and therefore s is chosen as the
build relation.
· A hash function h1 takes the join attribute value of each tuple in
s and maps this tuple to one of the n processors.
· Each processor Pi reads the tuples of s that are on its disk Di ,
and sends each tuple to the appropriate processor based on
hash function h1. Let si denote the tuples of relation s that are
sent to processor Pi .
· As tuples of relation s are received at the destination
processors, they are partitioned further using another hash
function, h2, which is used to compute the hash-join locally.
(Cont.)
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Partitioned Parallel Hash-Join (Cont.)
· Once the tuples of s have been distributed, the larger relation r
is redistributed across the m processors using the hash
function h1. Let ri denote the tuples of relation r that are sent to
processor Pi.
· As the r tuples are received at the destination processors, they
are repartitioned using the function h2 (just as the probe
relation is partitioned in the sequential hash-join algorithm).
· Each processor Pi executes the build and probe phases of the
hash-join algorithm on the local partitions ri and si of r and s to
produce a partition of the final result of the hash-join.
· Note: Hash-join optimizations can be applied to the parallel
case; e.g., the hybrid hash-join algorithm can be used to cache
some of the incoming tuples in memory and avoid the cost of
writing them and reading them back in.
Database Systems Concepts 17.27 Silberschatz, Korth and Sudarshan c 1997
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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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Parallel Nested-Loop Join (Cont.)
· The indexed nested-loop join can actually be overlapped with
the distribution of tuples of relation s, to reduce the cost of
writing the tuples of relation s to disk and reading them back.
· However, the replication of relation s must be synchronized
with the join so that there is enough space in in-memory
buffers at each processor Pi to hold the tuples of relation s that
have been received but not yet used in the join.
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Other Relational Operations
Parallelizing the evaluation of other relational operations:
Selection Example: (r)
·  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.
·  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.
· All other cases: the selection is performed in parallel at all the
processors.
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Other Relational Operations (Cont.)
Duplicate elimination
· Perform by using either of the parallel sort techniques; with the
optimization of eliminating duplicates as soon as they are
found during sorting.
· Can also partition the tuples (using either range- or
hash-partitioning) 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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Other Relational Operations (Cont.)
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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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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Handling Skew
One way to handle skew in joins with range-partitioning
· construct and store a frequency table (or histogram) of the
attribute values for each attribute of each relation.
· Construct a load-balanced range-partition vector using the
histogram
value
frequency
1­5 6­10 11­15 16­20 21­25
50
40
30
20
10
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Interoperation Parallelism
Pipelined Parallelism
· Consider a join of four relations: r1 1 r2 1 r3 1 r4
· Set up a pipeline that computes the three joins in parallel.
· Let processor P1 be assigned the computation of
temp1  r1 1 r2 and let P2 be assigned the computation of
r3 1 temp1.
· As P1 computes tuples in r1 1 r2, it makes these tuples
available to processor P2.
· Thus, P2 has available to it some of the tuples in r1 1 r2
before P1 has finished its computation. P2 can use those
tuples to begin computation of temp1 1 r3 even before r1 1 r2
is fully computed by P1.
· As P2 computes tuples in (r1 1 r2) 1 r3, it makes these tuples
available to P3, which computes the join of these tuples with r4.
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Factors Limiting Utility of Pipeline Parallelism
· Pipelined parallelism is useful because 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 (i.e., 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.
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Independent Parallelism
· Operations in a query expression that do not depend on each
other can be executed in parallel.
· Consider the join r1 1 r2 1 r3 1 r4.
· Compute temp1  r1 1 r2 in parallel with temp2  r3 1 r4.
· When these two computations complete, we compute:
temp1 1 temp2
· To get further parallelism, the tuples in temp1 and temp2 can
be pipelined into the computation of temp1 1 temp2, which is
itself carried out using pipelined join.
· Does not provide a high degree of parallelism; less useful in a
highly parallel system, although it is useful with a lower degree
of parallelism.
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Query Optimization
· Query optimization in parallel databases is significantly more
complex than query optimization in sequential databases.
· Cost models are more complicated, since we must take into
account partitioning costs and issues such as skew and
resource contention.
· When scheduling execution tree in parallel system, must
decide:
­ How to parallelize each operation and how many
processors to use for it.
­ What operations to pipeline, what operations to execute
independently in parallel, and what operations to execute
sequentially, one after the other.
· Determining the amount of resources to allocate for each
operation is a problem. E.g., allocating more processors than
optimal can result in high communication overhead.
Database Systems Concepts 17.38 Silberschatz, Korth and Sudarshan c 1997
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Query Optimization (Cont.)
· Long pipelines should be avoided as the final operation may
wait a lot for inputs, while holding precious resources
· The number of parallel evaluation plans from which to choose
from is much larger than the number of sequential evaluation
plans. Therefore heuristics are needed while optimization
· Two alternative heuristics for choosing parallel plans:
1. No pipelining and inter-operation pipelining; just parallelize
every operation across all processors.
­ Finding best plan is now much easier -- use standard
optimization technique, but with new cost model
2. First choose most efficient sequential plan and then choose
how best to parallelize the operations in that plan.
­ Can explore pipelined parallelism as an option
· Choosing a good physical organization (partitioning technique)
is important to speed up queries.
Database Systems Concepts 17.39 Silberschatz, Korth and Sudarshan c 1997
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Design of Parallel Systems
Some issues in the design of parallel systems:
· Parallel loading of data from external sources is needed in
order to handle large volumes of incoming data.
· Resilience to failure of some processors or disks.
­ Probability of some disk or processor failing is higher in a
parallel system.
­ Operation (perhaps with degraded performance) should be
possible in spite of failure.
­ Redundancy achieved by storing extra copy of every data
item at another processor.
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Design of Parallel Systems (Cont.)
· On-line reorganization of data and schema changes must be
supported.
­ For example, index construction on terabyte databases can
take hours or days even on a parallel system.
 Need to allow other processing
(insertions/deletions/updates) to be performed on relation
even as index is being constructed.
 Basic idea: index construction tracks changes and
"catches up" on changes at the end.
­ Also need support for on-line repartitioning and schema
changes (executed concurrently with other processing).
Database Systems Concepts 17.41 Silberschatz, Korth and Sudarshan c 1997