程序代写代做代考 database algorithm AI distributed system chain Chapter 17: Parallel Databases

Chapter 17: Parallel Databases

Parallel and Distributed Query Processing
Parallel Systems and Distributed Systems
I/O Parallelism
Parallel Query Processing
Distributed Query Processing

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Database System Concepts

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Parallel Systems
Parallel machines have become common and affordable
Prices of microprocessors, memory and disks have dropped sharply
Recent desktop computers feature multiple processors and this trend is projected to accelerate
Data storage needs are growing increasingly large
user data at web-scale
100’s of millions of users, petabytes of data
large volumes of data are collected and stored for analysis.
multimedia objects like images/videos
Large-scale parallel database systems increasingly used for:
storing large volumes of data
processing time-consuming decision-support queries
providing high throughput for query processing

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Database System Concepts

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Parallel Systems (cont.)
Parallel database systems consist of multiple processors and multiple disks connected by a fast interconnection network.
A coarse-grain parallel machine consists of a small number of powerful processors
A massively parallel or fine-grain parallel machine utilizes thousands of smaller processors.
Typically hosted in a data center
Two main performance measures:
throughput: number of tasks that can be completed in a given time interval
A system can improve throughput by processing many tasks in parallel
response time: amount of time it takes to complete a single task from the time it is submitted
A system can improve response time by performing subtasks of each task in parallel

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Database System Concepts

Speed-Up
Speedup
Parallelism is used to provide speedup, where tasks are executed faster because more resources are provided.
A fixed-sized problem executing on a small system is given to a system which is N-times larger.
speedup = small system elapsed time
large system elapsed time
Speedup is linear if equation equals N.

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Database System Concepts

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Scale-Up
Scaleup:
Parallelism is used to provide scaleup, where larger tasks are processed in the same amount of time by providing more resources.
Increase the size of both the problem and the system: N-times larger system used to perform N-times larger job
scaleup = small system small problem elapsed time
big system big problem elapsed time
Scale up is linear if equation equals 1.

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Database System Concepts

Factors Limiting Speedup and Scaleup
Speedup and scaleup are often sublinear due to:
Startup/sequential costs
Cost of starting up multiple processes and sequential computation before/after parallel computation may dominate computation time, if the degree of parallelism is high.
Interference
Processes accessing shared resources (e.g., system bus, disks, or locks) compete with each other, thus spending time waiting on other processes, rather than performing useful work.
Skew
It is often difficult to divide a task into exactly equal-sized parts, the way that the sizes are distributed is therefore skewed.
The service time for the single slowest step will determine the service time for the task as a whole.
Example: A task of size 100 is divided into 10 parts and one task happens to be of size 20, the speedup is only 5, not 10.

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Database System Concepts

Parallel Database Architecture:
Shared Nothing
Node consists of a processor, memory, and one or more disks
All communication via interconnection network
Can be scaled up to thousands of processors without interference.
Main drawback: cost of communication and non-local disk access; sending data involves software interaction at both ends.

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Database System Concepts

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Distributed Systems
A distributed system consists of loosely coupled sites (or nodes) that share no physical component
Data spread over multiple sites.

Homogeneous distributed database
Same software/schema on all sites
Goal: provide a view of a single database, hiding details of distribution
Heterogeneous distributed database
Different software/schema on different sites
Goal: integrate existing databases to provide useful functionality

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Database System Concepts

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Parallel and Distributed Query Processing
Parallel Systems and Distributed Systems
I/O Parallelism
Parallel Query Processing
Distributed Query Processing

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Database System Concepts

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I/O Parallelism
Reduce the time required to retrieve relations from disk by partitioning the relations on multiple disks, on multiple nodes.
Horizontal partitioning – tuples of a relation are divided among many nodes such that some subset of tuples resides on each node.
Partitioning techniques (number of nodes = n):
Round-robin:
Send the i th tuple inserted in the relation to node 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 node i.

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Database System Concepts

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I/O Parallelism (Cont.)

Range partitioning:
Choose an attribute as the partitioning attribute.
Choose a partitioning vector [v1, v2, …, vn-1].
Let x be the partitioning attribute value of a tuple.
Tuples with x < v1 go to N1 Tuples with x  vn-1 go to Nn Tuples such that vi  x < vi+1 go to Ni+1 Example: ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 11 Types of Skew Data-distribution skew: some nodes have many tuples, while others may have fewer tuples. Attribute-value skew Some partitioning-attribute values appear in 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 Imbalance, even without attribute-value skew Badly chosen range-partitioning 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. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 12 Handling of Skew (Cont.) A small skew can result in a significant decrease in performance. Skew becomes an increasing problem with a higher degree of parallelism. Example: Consider a relation of 1000 tuples. i) If it is divided into 10 equal parts, speedup = = 10 ii) If it is divided into 10 unequal parts and even one partition has 200 tuples, speedup = 5 iii) If it is divided to 100 equal parts, speedup = 100 iv) If it is divided into 100 unequal parts and even one partition has 40 tuples, speedup = 25 The loss of speedup due to skew increases with parallelism. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts Handling Skew in Range-Partitioning Data-distribution skew can be avoided with range-partitioning by creating balanced range-partitioning vectors Sort the relation on the partitioning attribute. Construct the partitioning vector by scanning the relation in sorted order as follows. After every 1/n of the relation has been read, the value of the partitioning attribute of the next tuple is added to the partitioning vector. n denotes the number of partitions to be constructed. Imbalances can result if duplicates are present in partitioning attributes.  Extra I/O overhead in doing the initial sort. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 14 Handling Skew using Histograms Balanced partitioning vector can be constructed from histogram, which can be stored in the system catalog. In a histogram, the values for the attribute are divided into a number of ranges, and with each range the histogram associates the number of tuples whose attribute value lies in that range.  Reduced I/O overhead. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 15 Handling Skew Using Virtual Node Partitioning Key idea: pretend there are several times (10x to 20x) as many virtual nodes as real nodes Virtual nodes are mapped to real nodes Tuples partitioned across virtual nodes using range-partitioning vector Hash partitioning is also possible Mapping of virtual nodes to real nodes Round-robin: virtual node i mapped to real node (i-1 mod n)+1 Mapping table: mapping table virtual_to_real_map[] tracks which virtual node is on which real node Allows skew to be handled by moving virtual nodes from more loaded nodes to less loaded nodes Both data distribution skew and execution skew can be handled Basic idea: If any normal partition would have been skewed, it is very likely the skew is spread over a number of virtual partitions. Skewed virtual partitions get spread across a number of nodes, so work gets distributed evenly! ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 16 Parallel and Distributed Query Processing Parallel Systems and Distributed Systems I/O Parallelism Parallel Query Processing Distributed Query Processing ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 17 Parallel Query Processing Interquery parallelism Different queries can be run in parallel with each other. Increases throughput; used primarily to scale up a database system to support a larger number of queries per second. The response times of individual queries are no faster. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts Intraquery Parallelism Our discussion of parallel algorithms assumes: read-only queries shared-nothing architecture: n nodes, N1, ..., Nn, each assumed to have disks and processors Execution of a single query in parallel on multiple nodes; important for speeding up long-running queries. Two complementary forms of intraquery parallelism: Intraoperation Parallelism Parallelize execution of each individual operation in a query, e.g., sort, select, project, join. Data can be partitioned and each node can work independently on its own partition. High degree of parallelism Interoperation Parallelism Execute different operations in a query in parallel. Limited degree of parallelism ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 19 Range-Partitioning Sort Suppose a relation is partitioned among nodes N1, ..., Nn. Choose nodes N1, ..., Nm to do sorting. Create range-partitioning vector with m-1 entries on the sorting attributes Redistribute the relation using range partitioning All tuples that lie in the ith range are sent to node Ni Ni stores the tuples it received temporarily on its local disk. This step requires I/O and communication overhead. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 20 Range-Partitioning Sort (cont.) Each node Ni sorts its partition of the relation locally. Data parallelism: each node executes same operation (sort) in parallel with other nodes, without any interaction with the others. Concatenate the results to get the fully sorted relation range-partitioning ensures that, if i < j, all key values in node Ni are all less than all key values in Nj. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 21 Parallel External Sort-Merge Suppose a relation is partitioned among nodes N1, ..., Nn. Each node Ni locally sorts the data. The sorted runs on each node are then merged in parallel to get the final sorted output. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 22 Parallel External Sort-Merge (Cont.) Parallelize the merging of sorted runs as follows: The sorted partitions at each node Ni are range-partitioned across the nodes N1, ..., Nm (all by the same partitioning vector) and the tuples are sent in sorted order, so each node receives the tuples as sorted streams. Each node Ni performs a merge on the sorted streams as they are received, to get a single sorted run. The sorted runs on nodes N1, ..., Nm are concatenated to get the final result. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 23 Parallel Join Reminder: 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. Basic idea: Divide the tuples of the input relations over several nodes. Each node then computes part of the join locally. The results from each node can be collected together to produce the final result. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 24 Partitioned Parallel Join For equi-joins and natural joins, it is possible to partition the two input relations across the nodes, and compute the join locally at each node. Let r and s be the input relations, and we want to compute r r.A=s.B s. r and s each is partitioned into m partitions, denoted r1’, r2’, ..., rm’ and s1’, s2’, ..., sm’. 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 node Ni. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 25 Partitioned Parallel Join (cont.) Join can be computed at each node using any of Hash join, leading to partitioned parallel hash join Merge join, leading to partitioned parallel merge join Nested loops join, leading to partitioned parallel nested-loops join or partitioned parallel index nested-loops join ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 26 Partitioned Parallel Hash-Join Parallelizing partitioned hash join: Assume relations r and s are partitioned and 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 nodes. Each node Ni reads the tuples of s that are on its local disk, and sends each tuple to the appropriate node based on hash function h1. Let si denote the tuples of relation s that are sent to node Ni. As tuples of relation s are received at the destination nodes, they are partitioned further using another hash function, h2, which is used to compute the hash-join locally. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts Partitioned Parallel Hash-Join (Cont.) Next, the larger relation r is redistributed across the n nodes using the hash function h1 Let ri denote the tuples of relation r that are sent to node Ni. As the r tuples are received at the destination nodes, they are repartitioned using the function h2 Each node Ni executes the build and probe phase 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. ©Silberschatz, Korth and Sudarshan ‹#› Database System Concepts 28 Fragment-and-Replicate Join Partitioning is not possible for some join conditions E.g., non-equijoin conditions, such as r.A > s.B.
In these cases, parallelization can be accomplished by fragment and replicate technique
Special case – asymmetric fragment-and-replicate:
One of the relations, say r, is partitioned using any partitioning technique.
The other relation, s, is replicated across all the nodes.
Node Ni then locally computes the join of ri with all of s using any join technique.
Also referred to as broadcast join

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Database System Concepts

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Fragment-and-Replicate Join (Cont.)
General case
Reduces the sizes of the relations at each node.
There must be at least m * n nodes.
Label the nodes as N1,1, N1,2, …, N1,m, N2,1, …, Nn,m.
r is partitioned into n partitions, r1, r2, …, rn
s is partitioned into m partitions, s1, s2, …, sm
Any partitioning technique may be used.
ri is replicated to Ni,1, Ni,2, …, Ni,m (a row)
si is replicated to N1,i, N2,i, …, Nn,i (a column)
Ni,j computes the join of ri with sj.
Any join technique can be used at each node Ni,j.

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Database System Concepts

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Fragment-and-Replicate Join (cont.)

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Database System Concepts

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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., if s is small and r is large, and already partitioned. It may be cheaper to replicate s across all nodes, rather than repartition r and s on the join attributes.

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Selection
Selection (r)
If  is of the form ai = v, where ai is an attribute and v is a value.
If r is partitioned on ai, the selection is performed at a single node.
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 node whose partition overlaps with the specified range of values.
In all other cases: the selection is performed in parallel at all the nodes.

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Database System Concepts

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Duplicate Elimination and Projection
Duplicate elimination
Perform by using either of the parallel sort techniques
eliminate duplicates as soon as they are found during sorting.
Or, partition the tuples (using either range- or hash- partitioning) and perform duplicate elimination locally at each node.
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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Database System Concepts

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Grouping/Aggregation
A straight-forward way:
partition the relation on the grouping attributes
compute the aggregate values locally at each node.
Optimization: Can reduce cost of transferring tuples during partitioning by partial aggregation before partitioning
Consider the sum aggregation operation:
Perform aggregation operation at each node Ni on those tuples stored on its local disk
results in tuples with partial sums at each node
there is one tuple at Ni for each value of the grouping attribute
Result of the local aggregation is partitioned on the grouping attribute, and the aggregation performed again on tuples with the partial sums at each node Ni to get the final result.
Fewer tuples need to be sent to other nodes during partitioning.

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Database System Concepts

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Interoperator Parallelism
Reminder: In pipelining, the output tuples of one operation, A, are consumed by a second operation, B, even before A has produced the entire set of tuples in its output.
Pipelined parallelism
Run A and B simultaneously on different nodes, so that B consumes tuples in parallel with A producing them.
Consider a join of four relations
r1 r2 r3 r4

r1
r2
r3
r4
Set up a pipeline that computes the three joins in parallel
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

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Factors Limiting Utility of Pipelined Parallelism
Pipelined parallelism is useful since it avoids writing intermediate results to disk
Useful with small number of nodes, but does not scale up well with more nodes.
Does not provide a high degree of parallelism since pipeline chains are not very long
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.

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Database System Concepts

Independent Parallelism
Independent parallelism
Operations in a query expression that do not depend on one another can be executed in parallel.
Consider a join of four relations
r1 r2 r3 r4
Let N1 be assigned the computation of temp1 = r1 r2
And N2 be assigned the computation of temp2 = r3 r4
And N3 be assigned the computation of temp1 temp2
N1 and N2 can work independently in parallel
N3 has to wait for input from N1 and N2
Can pipeline output of N1 and N2 to N3, 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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Database System Concepts

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Query Optimization for Parallel Execution
Reminder: A query optimizer takes a query and finds the cheapest execution plan.
Query optimization in parallel databases is significantly more complex than query optimization in sequential databases.
Different options for partitioning inputs and intermediate results
Cost models are more complicated, since we must take into account partitioning costs and issues such as skew and resource contention.

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Database System Concepts

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Parallel Query Plan Space
A parallel query plan must specify
How to parallelize each operation, including which algorithm to use, and how to partition inputs and intermediate results
How the plan is to be scheduled
How many nodes to use for each operation
What operations to pipeline within same node or different nodes
What operations to execute independently in parallel, and
What operations to execute sequentially, one after the other.
E.g., In query r.A 𝛾sum(s.C)(r ⋈ r.A=s.A ˄ r.B=s.B s)
Partitioning r and s on (A,B) for join will require repartitioning for aggregation
But partitioning r and s on (A) for join will allow aggregation with no further repartitioning
Query optimizer has to choose best plan taking above issues into account

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Choosing Query Plans
The number of parallel evaluation plans from which to choose from is much larger than the number of sequential evaluation plans.
Two alternatives often used for choosing parallel plans:
First choose most efficient sequential plan and then choose how best to parallelize the operations in that plan
Heuristic, since best sequential plan may not lead to best parallel plan
Parallelize every operation across all nodes

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Database System Concepts

Parallel and Distributed Query Processing
Parallel Systems and Distributed Systems
I/O Parallelism
Parallel Query Processing
Distributed Query Processing

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Database System Concepts

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Distributed Query Processing
Many database applications require data from multiple databases.
For centralized systems, the primary criterion for measuring the cost of a particular strategy is the number of disk accesses.
In a distributed system, other issues must be taken into account:
The cost of a data transmission over the network.
The potential gain in performance from having several sites process parts of the query in parallel.

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Database System Concepts

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Join Locations and Join Ordering
Consider the following relational algebra expression
r1 ⨝ r2 ⨝ r3
r1 is stored at site S1
r2 at S2
r3 at S3
For a query issued at site SI, the system needs to produce the result at site SI

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Possible Query Processing Strategies
Strategy 1
Ship copies of all three relations to site SI and choose a strategy for processing the entire locally at site SI.
Strategy 2
Ship a copy of the r1 relation to site S2 and compute
temp1 = r1 ⨝ r2 at S2.
Ship temp1 from S2 to S3, and compute
temp2 = temp1 ⨝ r3 at S3
Ship the result temp2 to SI.
Devise similar strategies, exchanging the roles S1, S2, S3
Must consider following factors:
amount of data being shipped
cost of transmitting a data block between sites
relative processing speed at each site

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Semijoin Strategy
Let r1 be a relation with schema R1 stored at site S1
Let r2 be a relation with schema R2 stored at site S2
Evaluate the expression r1 ⨝ r2 and obtain the result at S1.
Strategy 1:
Ship r2 to S1. However, if there are many tuples of r2 that do not join with any tuple of r1, then this entails shipping useless tuples.
Strategy 2:
1. Compute temp1  R1  R2 (r1) at S1.
2. Ship temp1 from S1 to S2.
3. Compute temp2  r2 ⨝ temp1 at S2.
4. Ship temp2 from S2 to S1.
5. Compute r1 ⨝ temp2 at S1. This is the same as r1 ⨝ r2.

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Database System Concepts

Semijoin Strategy (Cont.)
Strategy 2
temp2 contains all of the tuples that qualify the join condition but other attributes of r1 are missing
Cost savings: ship only temp2, rather than all of r2 to S1
versus
Overhead: ship temp1 to S2.
Particularly advantageous when relatively few tuples of r2 contribute to the join
temp2 may have significantly fewer tuples than r2.
overhead will be dominated by savings

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Database System Concepts

Semijoin Strategy (Cont.)
The semijoin of r1 with r2, is denoted by:
r1 ⋉ r2
it is defined by:
R1 (r1 ⨝ r2)
Thus, r1 ⋉ r2 selects those tuples of r1 that contributed to r1 ⨝ r2.
In step 3 above, temp2=r2 ⋉ r1.
For joins of several relations, the above strategy can be extended to a series of semijoin steps.

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Distributed Query Optimization
Extensions to existing query optimization techniques
Record the location of data
Annotate operators with the site where they are executed
Operators typically operate only on local data
Remote data is typically fetched locally before operator is executed
Consider semijoin operations to reduce data transfer costs
Heuristic: restrict semijoins only on database tables, not on intermediate join results

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Database System Concepts

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