Institut für Scientific Computing – Universität Wien
P.Brezany
FragmentationFragmentation
Univ.-Prof. Dr. Peter Brezany
Institut für Scientific Computing
Universität Wien
Tel. 4277 39425
Sprechstunde: Di, 13.00-14.00
Institut für Scientific Computing – Universität Wien
P.Brezany
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Introduction
•We already presented the various fragmentationstrategies.
•Fragmentation strategies:
–horizontal
–vertical
–nesting fragments in a hybrid fashion.
Institut für Scientific Computing – Universität Wien
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Horizontal Fragmentation
•Primary horizontal fragmentation of a relation isperformed using predicates that are defined on thatrelation.
•Derived horizontal fragmentation is the partitioning of arelation that results from predicates being defined onanother relation.
•Information requirements of horizontal fragmentation
–Database information
–Application information
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Database Example
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Database Information
•It concerns the global conceptual schema. In this context it isimportant to note how the database relations are connected to oneanother, especially with joins.
•Example:
Given link L1 of the above figure, the owner and member functions have the
the following values: owner(L1) = PAY; member(L1) = EMP
The quantitative information required about the database is the cardinality
of each relation R, denoted card(R).
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Application Information
•It is required:
–qualitative information, which guides the fragmentation activity
–quantitative information is incorporated primarily into the allocation models.
•The fundamental qualitative information consists of the predicates usedin user queries.It is not possible to analyze all of the user applicationsto determine these predicates one should at least investigate themost “important“ ones. a rule of thumb: the most active 20% ofuser queries account for 80% of the total data access.
•Simple predicates: Given a relation R(A1, A2, ..., An), where Ai is anattribute defined over domain Di, a simple predicate pj defined on Rhas the form
pj : Ai Value
where {, , , , , } and Value Di. We use Pri to denote the setof all simple predicates defined on a relation Ri. The members of Priare denoted by pij.
Example: for the relation instance PROJ:
PNAME = “Maintenance“ BUDGET 200000
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Application Information (cont.)
User queries often include more complicated predicates, which are
Boolean combinations of simple predicates.
One important combination: minterm predicate – conjunction of
simple predicates.
Given a set of simple predicates for relation
Ri, the set of minterm predicates is defined as
where
or
So each simple predicate can occur in a minterm predicate either
in its natural form or ist negated form.
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Application Information (cont.)
Example:
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Application Information (cont.)
•In terms of quantitative information about the userapplications, we need to have 2 sets of data:
1.Minterm selectivity: number of tuples of the relation that wouldbe accessed by a user query specified according to a givenminterm predicate. E.g., in previous example, sel(m1)=0 sincethere are no tuples in PAY that satisfy the minterm predicate.sel(m2)=1
2.Access frequency: frequency with which user applications accessdata. If Q = {q1, q2, ..., qq} is a set of user queries, acc(qi)indicates the access frequency of query qi in a given period.
•The minterm access frequencies can be determinedfrom the query frequencies acc(mi) – the accessfrequency of a minterm mi.
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Primary Horizontal Fragmentation
•It is defined by a selection operation on the owner relations ofa database schema.
•Given a relation R, its horizontal fragments are given by
Ri = Fi(R), 1 i w
where Fi is the selection formula used to obtain fragment Ri.
Example : PROJ PROJ1 and PROJ2
PROJ1 = BUDGET 200000(PROJ)
PROJ2 = BUDGET 200000(PROJ)
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Primary Horizontal Fragmentation (cont.)
Example:
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Primary Horizontal Fragmentation (cont.)
A more formal definition of a horizontal fragment:
•A horizontal fragment of relation Ri consists of all the tuplesof R that satisfy a minterm predicate mj.
•Hence, given a set of minterm predicates M, there are asmany horizontal fragments of R as there are mintermpredicates. minterm fragments.
•An important aspect of simple predicates is theircompleteness; another is their minimality.
•A set od simple predicates Pr is said to be complete if andonly if there is an equal probability of access by everyapplication to any tuple belonging to any minterm fragmentthat is defined according to Pr.
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Primary Horizontal Fragmentation (cont.)
•Example: Consider the fragmentation of PROJ in the lastexample. If the only application that accesses PROJwants to access the tuples according to the location, theset is complete since each tuple of each fragment PROJi,has the same probability of being accessed.
•If there is a second application which accesses only thoseproject tuples where the budegt is less than $200.000,then Pr is not complete. Some of the tuples within eachPROJi have a higher probability of being accessed due tothis second application.
•To make the set of predicates complete, we need to add(BUDGET 200000, BUDGET > 20000) to Pr:
Pr = {LOC=“Montreal“, LOC=“New York“, LOC=“Paris“,
BUDGET200000, BUDGET > 20000}
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Primary Horizontal Fragmentation (cont.)
•The second desirable property of the set ofpredicates, according to which minterm predicates andturn, fragments are to be defined, is minimality.
•If a predicate influences how fragmentation isperformed (i.e., causes a fragment f to be furtherfragmented into, say, fi and fj), there should be atleast one application that accesses fi and fjdifferently. In other words, the simple predicateshould be relevant in determining a fragmentation.
•If all the predicates of a set Pr are relevant, Pr isminimal.
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Primary Horizontal Fragmentation (cont.)
•Example:
The set Pr defined in the previous example iscomplete and minimal. If, however, we were to
add the predicate
PNAME = „Instrumentation“
to Pr, the resulting set would not be minimal sincethe new predicate is not relevant with respect toPr. There is no application that would access theresulting fragments any differently.
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Derived Horizontal Fragmentation
A derived horizontal fragmentation is defined on a member
relation of a link according to a selection operation specified onits owner.
Given a link L where owner(L) = S and member(L) = R, the derived
horizontal fragments of R are defined as
Ri = R Si, 1 i w
where w is the maximum number of fragments that will bedefined on R, and Si = Fi(S), where Fi is the formula according towhich the primary horizontal fragment Si is defined.
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Derived Horizontal Fragmentation (cont.)
Example: Consider link L1, where
owner(L1) = PAY and
member(L1) = EMP.
Then we can group engineers into
2 groups according to theirsalary:
$30.000 and > $30.000. The 2fragments
EMP1 and EMP2 are defined:
EMP1 = EMP PAY1
EMP2 = EMP PAY2
where
PAY1 = SAL30000 (PAY)
PAY2 = SAL>30000 (PAY)
Derived horizontal fragmentation of EMP