Determination of Semi-Join Programs in SDD-1

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Determination of Semi-Join Programs in SDD-1

• In the SDD-1 approach semi-joins are used for reducingIn the SDD 1 approach, semi joins are used for reducing cardinalities of relation; when they have been applied to the maximum extent, all relations are collected at the same site,

h b t d

where query can be executed.

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Basic SDD-1 Algorithm

• The Basic SDD-1 Algorithm constructs reducers program for relations; reducers consists of unary operations &

semi-joins, which are selected on the basis of their cost.j , • Consider the semi-join R SJ_A=B S; it has no cost when R

& S are stored at the same site.

• When R & S are at different site cost is

Cost(R SJ_A=B S) = C₀ + val(B[S]) X size(B) X C₁ • The benefit of semi-join

• The benefit of semi-join

benefit(R SJ_A=B S)= (1 - ρ) X size(R) X card(R) X C₁ where ρ is the selectivity of the semi-join.

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• The algorithm can be given as follows

1 Basis : A join graph G is given All local

1. Basis :- A join graph G is given. All local

reductions to relations appearing in the G

have been applied already

have been applied already.

2. Method :- While there are profitable

semi-joins include either most profitable

semi joins, include either most profitable

or the cheapest one in the reducer

program of the relation to which it

p g

applies, reevaluate benefits and costs of

the affected semi-joins.

3. Termination :- The site which requires

less transmission is selected for

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Query optimization using SDD-1 algorithm

Definition of Optimization Problem

SNUM=SNUM DEPTNUM=DEPTNUM

Site(SUPPLIER) = 1 Site(SUPPLY) = 2 Site(DEPT) = 3

SNUM NAME DEPTNUM NAME

All values of SNUM in SUPPLIER are present in SUPPLY All values of SNUM in SUPPLIER are present in SUPPLY All values of DEPTNUM in DEPT are present in SUPPLY

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Description of all possible semi-joins

S i j i S l ti it B fit C t

Semi-joins Selectivity Benefits Cost p1:SUPPLY NSJ SUPPLIER ρ(p1) = 0 2 0 8X6X5000 4X200 p1:SUPPLY NSJ SUPPLIER ρ(p1) = 0.2 0.8X6X5000 4X200 p2:SUPPLY NSJ DEPT ρ(p2) = 0.2 0.8X6X5000 2X20 p3:SUPPLIER NSJ SUPPLY ρ(p3) = 1 - 4x1000

p3 SU SJ SU ρ(p3) 000

p4: DEPT NSJ SUPPLY ρ(p4) = 1 - 2X100

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• Iteration 1 : p2 selected

• Effect on the profile of SUPPLYp

Card(SUPPLY) = 1000

Site(SUPPLY) = 2 C(n,m,r) used for SNUM,_{with n= 5000, r=1000}

l(SNUM[SUPPLY]) 1000

Effect on other Semi-joins Selectivity Benefits Cost

p1:SUPPLY NSJ SUPPLIER ρ(p1) = 0.2 0.8X6X5000 4X200 3 SUPPLIER NSJ SUPPLY ( 3) 0 666 0 333X24X200 4 666 p3:SUPPLIER NSJ SUPPLY ρ(p3) = 0.666 0.333X24X200 4x666 p4: DEPT NSJ SUPPLY ρ(p4) = 1 - 2X20

Profitable semi-joins: p1 & p3

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• Effect on the profile of SUPPLYp

Card(SUPPLY) = 200 Site(SUPPLY) = 2

C(n,m,r) used for DEPTNUM, with n= 1000, r=200

m=val(deptNUM[SUPPLY’])=20 SNUM DEPTNUM

SIZE 4 2

( ) _{m=val(deptNUM[SUPPLY ])=20}

r, for r < m/2

p3:SUPPLIER NSJ SUPPLY ρ(p3) = 0.666 0.333X24X200 4x123

4 SUPPLY NSJ DEPT ( 4) 1 2X20

p4:SUPPLY NSJ DEPT ρ(p4) = 1 - 2X20

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• Effect on the profile of SUPPLIERp

Card(SUPPLIER) = 123 Site(SUPPLIER) = 1

SNUM NAME

SIZE 4 20

( )

SIZE 4 20 VAL 123 123

p4:SUPPLY NSJ DEPT ρ(p4) = 1 - 2X20

No other Profitable semi-joins

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Selection of the site

f

ll

ti

ll th

l ti

for collecting all the relations

Cost(site 1) = 6 X 200

+ 5 X 20 = 1300

Cost(site 2) = 24 X 123 + 5 X 20 = 3052

Cost(site 2) 24 X 123 + 5 X 20

3052

Cost(site 3) = 24 X 123 + 6 X 200 = 4152

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Postoptimization

• To improve the obtained solution a

• To improve the obtained solution, a

postoptimization can be made. The

postoptimization obeys two criteria

1. Eliminating the semi-joins whose only effect is

to reduce relations that are already on the site

selected for executing the query.

2 Delaying expensive semi-joins R

SJ

S after

2. Delaying expensive semi joins R

SJ

S after

reduction of S by means of other semi-joins;

this requires changing the order of application

q

g g

pp

of semi-join operations.

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Cont… Example

Postoptimi ation

• Postoptimization

Since semi-join p3 has the only effect of

reducing relation SUPPLIER, which is at the

selected site 1, p3 is not useful.

• Summary

Summary

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Apers, Hevner and Yao (AHY)

algorithm

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General Queries

• General queries are the queries with joins &

unions in their optimization graph.

• The basic transformation criteria used is the

commutativity of Join & Unions for

y

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Effect of Commuting Joins & Unions

The commutation of joins & unions can be represented in The commutation of joins & unions can be represented in figure, which represents three different optimization graph of same query.

I fi ( ) f t fi t ll t d th j i d ll d

In fig (a), fragments are first collected then joined, called as nondistributed join.

In fig (b), fragments are first joined then collected, called as distributed join.

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1. Nondistributed join :- This optimization problem is much

simpler. It reduces to determining a pair of sites

(possibly the same site) at which union operations are

performed. If the sites are different, then the query is

reduced to a simple join query between two relations

reduced to a simple join query between two relations.

2. Distributed join :- This optimization problem is much

harder. The join graph of join between R and S within

j

g p

j

hypernode representing the union operation.

The knowledge of fragmentation criteria must be used

for eliminating edges from join graph.

Once minimal join graph has been determined, the

execution of joins appearing in the join must be

optimized.

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• It is also possible to perform Partial Unions,

before performing joins (as in fig(c)).

p

g j

(

g( ))

• In building optimization graph G’ of fig (C) from

optimization graph G of fig (b), following rules are

op

a o g ap G o

g (b), o o

g u es a e

used.

1.Fragment on which partial unions are performed

are enclosed into hypernode

( {R1, R2} & {S2, S3}).

( {

,

}

{

,

})

2.If two fragments Ri & Sj are connected by an arc

in G, then the nodes to which they belong are

,

y

g

also connected by an arc in G’.

(Edge between R1 & S2 in G generates the edge

(

g

between {R1, R2} & {S2, S3})

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• Partitioned join graphs are a important class of

join graphs for optimization.

j

g p

p

• In the Partitioned join graphs, each subgraph can

independently optimized due to facts

depe de

y op

ed due o ac s

– The optimization of joins of disconnected subgraphs

can be performed independently.

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• This property allows the building of a variety of

strategies involving partial unions for each

g

g p

operation

.

• Searching for the best execution of a given query

g

q

y

requires.

– Generating all the possible query optimization graphs.

A l i j i i th d t ti i j i & ddi t f

– Applying join queries methods to optimize joins & adding cost of unions.

– Selecting the best query processing policy among them.

• The figure shows the four alternative ways of computing

the cost of join graph of two relations R & S having two

f

t

h

fragment each.

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