We define a standard of effectiveness for a database calculus relative to a query language. Effectiveness judges suitability to serve as a processing framework for the query language, and comprises aspects of coverage, manipulability and efficient evaluation. We present the monoid calculus, and argue its effectiveness for object-oriented query languages, exemplified by OQL of ODMG-93. The monoid calculus readily captures such features as multiple collection types, aggregations, arbitrary composition of type constructors and nested query expressions. We also show how to extend the monoid calculus to deal with vectors and arrays in more expressive ways than current query languages do, and illustrate how it can handle identity and updates. 1 Introduction A much-touted advantage of the relational data model is the existence of a formal calculus and algebra to model database queries. In practice, these formalisms fail to model many of the features present in commercial query languages (e.g...

This paper concentrates on query unnesting (also known as query decorrelation), an optimization that, even though improves performance considerably, is not treated properly (if at all) by most OODB systems. Our framework generalizes many unnesting techniques proposed recently in the literature and is capable of removing any form of query nesting using a very simple and efficient algorithm. The simplicity of our method is due to the use of the monoid comprehension calculus as an intermediate form for OODB queries. The monoid comprehension calculus treats operations over multiple collection types, aggregates, and quantifiers in a similar way, resulting in a uniform way of unnesting queries, regardless of their type of nesting.

Parallel computers have been successfully deployed in many scientific and numerical application areas, although their use in non-numerical and database applications has been scarce. In this report, we first survey the architectural advancements beginning to make general-purpose parallel computing cost-effective, the requirements for non-numerical (or symbolic) applications, and the previous attempts to develop parallel databases. The central theme of the Bulk Synchronous Parallel model is to provide a high level abstraction of parallel computing hardware whilst providing a realisation of a parallel programming model that enables architecture independent programs to deliver scalable performance on diverse hardware platforms. Therefore, the primary objective of this report is to investigate the feasibility of developing a portable, scalable, parallel object database, based on the Bulk Synchronous Parallel model of computation. In particular, we devise a way of providing high-level abstra...

The use of approximations of complex, possibly nested collection, objects can considerably improve the processing of queries with expensive predicates. The improvement is gained by (1) avoiding much of unnecessary evaluation of expensive predicates, and (2) enabling the use of a significantly wider range of special-purpose algorithms, and indexing techniques working on approximations of objects. This paper develops a necessary query transformation infrastructure for such approximationbased query processing, in presence of extensible family of collection types, aggregation functions, indices and special purpose algorithms. The approximation-based filtering is formalized by the notion of a filtering graph, whose arcs describe, intuitively, under which conditions a filtering predicate can be added before a predicate in a query. Next, two pre-processing mechanisms, the inverse grouping and approximation grouping are introduced to facilitate a direct retrieval of nested collection objects by testing their internal components, their transformations or approximations. Query transformation rules corresponding the filtering graph and the groupings are presented using a variation of monoid comprehension calculus. While the filtering graph and the groupings are powerful tools in optimization, the filtering graph must, in general, be provided the application programmer. However, this paper introduces and studies a very expressive family of constraint objects, for which the filtering graph and inverse and approximation groupings can be derived automatically. The paper also constructs complex query transformation templates which are derived from the basic transformation rules for filtering graphs, and for the two pre-processing mechanisms.

Syntax of Object Comprehensions Es ::= E j E , Es E ::= E union E j E differ E j [ Xs --- E ] j E and E j E or E j not E j E hasClass E j E hasClass E with E j Y E ! Y E j E / E j E . E j I( Es ) j I j K j f Es g j f E : : : E g j E . [ E ] j A E j ( E ) Xs ::= j X j X ; Xs X ::= D j L j E D ::= I / E L ::= I as E Y ::= j some j atleast E j just E j atmost E j every A ::= size ::= set j bag j list ! ::= = j = j ? j ?= j ! j != j == j == / ::= * j / j + j - B Abstract Syntax of Function Arguments F ::= I . E j F ffi F Es ::= E j E, Es E ::= E . E j I( Es ) j E ff E j E ! E j E / E j I j K j ( E ) j Q ff ::= j j : ! ::= = j = j ? j ?= j ! j != / ::= * j / j + j - 22 References ...

This thesis proposes an object-oriented query language that is more powerful than many existing query languages. The language is formally specified and its expressive power is demonstrated by giving four translation schemes from other prominent objectoriented query languages. Further, this query language can be supported by a query algebra and both the query language and query algebra can be optimised using meaning preserving transformation rules. Object-Oriented Query Languages. The functional requirements of high-level objectoriented query languages are identified and they combine as well as supplement features found in existing object-oriented query languages. Effectively they formulate a query model against which existing query languages can be evaluated and compared. An evaluation of four representative query languages chosen from research prototypes and commercial products shows that none satisfies all the requirements. On the basis of the requirements a new query language, obje...

Query language and querying facilities are critical factors for wide acceptance of Object-Oriented Database Management Systems (OODBMS) in the market. In this paper, we focus on query model on an aggregation hierarchy. We call this query "Aggregation Query". Query on an aggregation hierarchy is unique and differs from general query on association relationships. The latter is often known as path expression query. The difference is analogous to the distinction between association and aggregation in object modelling. In our proposal, we present three important elements of aggregation query, particularly (i) aggregation query hierarchy, (ii) shorthand path expression for aggregation query utility, and (iii) retrieving aggregation tree. Whilst the first element above is adopted from path expression queries, the second element is an extension to general path expression query, and the third element is unique to aggregation, as aggregation resembles a Part-Of relationship, which is more specialized than association relationships.