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/* Field limit */ INTEGRITY Partsweight > 0; /* Reference */ INTEGRITY Employeedept = Departmentsname /* Unique key: tokens = types */ INTEGRITY COUNT ALL(Partsp id) = COUNT DISTINCT(Partspid); /* Complete ownership: owned types = owner tokens */ INTEGRITY COUNT DISTINCT(Supplyp id) = COUNT ALL(Partsp id);
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468 9-2-6 File Support
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Database Implementation
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Many relational implementations use simple le structures When the mapping of relational tables to les is one-to-one, the le records will have a xed number of elds If the elds are also restricted to be of xed length, the records will also be of xed length If data values can be variable, or if more complex mapping from relations to les is permitted, the demands on the supporting les increase
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For instance, one SQL row is stored as one record, but SQL/DS does permit variablelength strings, up to 32 767 characters, and hence needs variable-length-record support This support is provided by VSAM (Sec 4-3), and the index structure of VSAM also provides the maintenance for indexed attributes
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Statistical descriptive information is maintained by SQL, so that a decision can be made whether to use indexes or sorting to perform the join Estimates about the expected partitioning e ectiveness of selection clauses on attributes, or selectivity, provide information used to reorder the primitive operations into which a complex query may be decomposed We consider this aspect in Sec 9-2-7 To provide the capability for recovery of a transaction, log les may be speci ed to collect all inputs and a ected records These logs are also VSAM les The principles and the use of logs are presented in Secs 11-3 and 11-4 The existence of a log permits the ROLLBACK operation mentioned in Table 9-3 The allocation and extension of space for an SQL database is handled by a set of commands which direct VSAM Multiple tables can share a single le space The information is itself collected in SQL TABLES and used during operation of the database, so that the user does not have to be concerned about the underlying le structure The INGRES implementation cited in Secs 9-2-2 and 9-2-5 provides four alternative le types to the system implementor All records are of xed length For each relation to be implemented the le type may be either a HEAP similar to a pile, a HEAPSORT similar to sequential le, ISAM an indexed sequential le, or HASH a direct le The le implementation choice determines if the stored data is kept as a table (HEAP) or as a relation (HEAPSORT, ISAM, HASH), according to the de nitions shown in Example 9-3 The ORACLE system, which uses SEQUEL, the query language used in the development system which preceded SQL/DS, implements its les using a hierarchical organization, similar to DL/1 les
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9-2-7 The Execution of Calculus Statements In order to execute the statements of the relational calculus, a transformation to a sequence of relational operations is required The operations are essentially those described in Sec 7-4, perhaps modi ed to deal with tables instead of relations The parsing of the calculus statements is similar to the problem faced by compilers, with the additional consideration that reordering of clauses is possible and sometimes necessary Reordering is also part of the compiling process for other nonprocedural languages which describe relationships, and is seen in simulation languages
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The execution of the statements requires a capable and sophisticated DBMS if adequate e ciency is to be obtained A high degree of optimization is possible in the relational calculus by rearranging the clauses into an optimal sequence The general rule is to rst reduce the number of records to be accessed by exploiting indexes for attributes appearing in restricting WHERE clauses When multiple restriction clauses are available and have indexes, the clause with the greatest expected partitioning e ectiveness should be chosen rst The partitioning e ectiveness of an attribute could be kept in a schema entry using a suitable encoding A practical problem is that di erent values within one attribute have greatly di ering power
If, for instance, we wish to nd personnel in a relation identi ed by p for a construction task in Alaska, (pname,pdep no) WHERE (psex="Male" pexperience>10) then the predicate experience>10 should be evaluated rst, since we can expect that this will leave a smaller intermediate relation than predicate sex="Male" In the case above, the value Female applied to construction workers will in all probability retrieve a much smaller intermediate result than the WHERE clause does now
Intermediate results are often not materialized into intermediate relations It is often more e ective to process result tuples further, and so avoid repetitive storing and retrieval of intermediate values Whenever possible the TIDs of the database records will be manipulated, since a large number of TIDs can be kept in memory When a record containing the tuple is located, all required attributes are projected to reduce the tuple size but avoid any further record access Cross-product and join operations, which have the potential to generate large intermediate results, are typically scheduled last If the number of tuples satisfying the join condition or join selectivity can be estimated, however, and appears low, joins may be performed earlier Along a connection a join result will never be greater than the larger relation The eventual choice of execution sequence for a query is determined by minimization of the total cost of all operations required to carry out the query In a transaction with multiple embedded queries yet better performance is possible by an overall optimization Within a transaction the queries may refer to di erent aspects of a similar subset of data, so that a single retrieval from the database les can serve multiple queries
An airline transaction may rst retrieve the times of the ights between two points, and then, conditionally, the seat availability and the cost of the ight A single retrieval can obtain all potentially relevant data at a low incremental cost and can greatly reduce the average transaction cost
The overall e ect of query optimization in a relational system will depend greatly on the variability of the access patterns It is di cult to beat a system with de ned connections along a query path, as we encountered in Sec 8-3, when the query matches the de ned physical structure and the database is reasonably large For unexpected queries, however, the optimization will provide much better performance than a system designed to address a di erent pattern will provide , etc) can vary a great deal from The cost of the relational operations ( , simplistic approaches to methods that exploit optimal algorithms and locality We will discuss these in the next section with the relational algebras
470 9-3
Database Implementation RELATIONAL ALGEBRA IMPLEMENTATION Union, intersection, and di erence of matching relations, ( , , ) Projection by domains ( ) Selection of tuples ( ) Join of arbitrary relations ( )
We encountered in Sec 7-4 the basic operations of the relational algebra:
These operations, together with the comparison and boolean operators used in the quali cation statements of the relational calculus, provide the tools for systems based on the relational algebra These systems may be used to support a relational calculus or can be made directly available to users Their nature is inherently procedural and these systems are comparable with systems using multiple unlinked nonhierarchical les and conventional data-processing operations An important early implementation based on a relational algebra is the Prototype Relational Test Vehicle (PRTV) We encountered it in Sec 7-4-1 when discussing the relational di erence operation The systems seen today range from small to large, from microcomputers to large systems for multiple users An early APL implementation of a relational algebra was limited to numeric data values and had no schema; attributes were referenced using column indexes Some systems based on the relational algebra, RDMS, which will be used for our rst examples, are in routine data-processing use at MIT 9-3-1 Relational Manipulations In the relational algebraic systems the computations are speci ed and carried out statement by statement There will be a greater use of workspaces and there is no need for tuple variables Selection is generally made available through WHERE clauses, but these will apply only to attributes of the referenced relation The syntax di ers greatly among these systems; the functions are nearly the same Some systems implement relations only as sets with distinct tuples; others permit more general tables Some of the more competent systems permit complex expressions of relational primitives, and then may try to minimize record accesses The query for employees of Example 9-4 to locate parents with children of school age can be presented to RDMS as follows:
Fathers(name) = PROJECT(Children WHERE age c = 6 BY father); Output(name,dep no) = COMPOSE(PROJECT(Employee BY(name,dep no)),Fathers)
COMPOSE(r1,r2)is a natural join operation using matching attribute names PROJECT(r BY a)speci es projection ra Additional relational and aggregation operators are available The statements can be part of programs to be executed together or can be used as commands entered on a terminal and executed immediately RDMS also provides facilities for self-contained use of the database through the use of inquiry packages and report generators Other operations seen in relational algebras are also provided We need union, intersection, di erence, and cartesian product:
Sec 9-3
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