Multivariable Expressions

Multivariable Expressions

Strategies for the evaluation of multivariable expressions are the largest building blocks for a general query-processing system. Two basic approaches exist, which are referred to as parallel processing and stepwise reduction. The parallel processing of query components serves to avoid repeated access to the same data. Repeated access to the same data can be avoided by simultaneous evaluation of multiple-query components. In Palermo [1972], all monadic terms associated with a variable are completely evaluated and all dyadic terms in which the same variable appears are partially processed concurrently with scanning of the range relation of the variable. Even AND –connections existing among the terms can be evaluated in parallel, which further reduces thesize of intermediate results [Jarke and Schmidt 1982]. A similar approach on a higher level has been described by Klug [1982b] in which aggregate functions and complex subqueries are computed in parallel. Scheduling strategies for the parallel processing of query components are discussed by Schmidt [1979].

Pipelining operations that can work on the partial output of preceding operations is another technique that exploits parallel processing opportunities [Smith and Chang 1975; Yao 1979]. For example, restriction and projection can be pipelined so that only a relatively small buffer for data exchange is required rather than the creation and subsequent reading of a possibly large temporary relation. Aspects of simultaneous evaluation and pipelining are combined in the so-called "feedback" method [Clausen 1980; Rothnie 1974, 1975], which uses partial results of a join operation in order to restrict its input.

The degree to which this can be done depends on...

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...th semijoins that achieve very strong reduction [Chiu and Ho 1980; Chiu et al. 1981].

Strategies for the evaluation of tree expressions containing both existential and universal quantifiers must take into account the order in which these quantifiers appear in the expression. Stepwise reduction is possible only when the processing of the edges of the query tree (breadth-first leaf-to-root) corresponds to the order of the quantifiers in the expression (right to left).

Methods for the efficient implementation of operations, such as the ones presented in this section, are candidates for hardware components in specialized database machines. However, such components often allow parallelism and therefore require somewhat different join and semijoin algorithms [Bitton et al. 1983; Maekawa 1982; Missikoff and Scholl 1983; Valduriez 1982; Valduriez and Gardarin 1984].