| dc.description.abstract | Support of order in query processing is a crucial component in
relational database systems, not only because the output of a
query is often required to be sorted in a specific order, but also
because employing order properties can significantly reduce the
query execution cost. Therefore, finding an effective approach to
answer queries over ordered data is important to the efficiency of
query processing in relational databases.
In this dissertation, an ordered relational database model is
proposed, which captures both data tuples of relations and tuple
ordering in relations. Based on this conceptual model, ordered
relational queries are formally defined in a two-sorted first-order calculus, which serves as a yardstick to evaluate
expressive power of other ordered query representations.
The primary purpose of this dissertation is to investigate the
expressive power of different ordered query representations.
Particularly, the completeness problem of ordered relational
algebras is studied with respect to the first-order calculus:
does there exist an ordered algebra such that any first-order expressible ordered
relational query can be expressed by a finite sequence of ordered
operations? The significance of studying the completeness problem
of ordered relational algebras is in that the completeness of
ordered relational algebras leads to the possibility of
implementing a finite set of ordered operators to express all
first-order expressible ordered queries in relational databases.
The dissertation then focuses on the completeness problem of
ordered conjunctive queries. This investigation is performed in an
incremental manner: first, the ordered conjunctive queries with
data-decided order is considered; then,
the ordered conjunctive queries with t-decided order is
studied; finally, the completeness problem for the general ordered
conjunctive queries is explored. The completeness theorem
of ordered algebras is proven for all three classes of ordered
conjunctive queries.
Although this ordered relational database model is only
conceptual, and ordered operators are not implemented in this
dissertation, we do prove that a complete set of ordered operators
exists to retrieve all first order expressible ordered queries in
the three classes of ordered conjunctive queries. This research
sheds light on the possibility of implementing a complete set of
ordered operators in relational databases to solve the performance
problem of order-relevant queries. | en |
