We consider the class of path-conjunctive queries and constraints (dependencies) defined over complex values with dictionaries.

We present an optimization method and algorithm designed for three objectives: physical data independence, semantic optimization, and generalized tableau minimization. The method relies on generalized forms of chase and "backchase" with constraints (dependencies). By using dictionaries (finite functions) in physical schemas we can capture with constraints useful access structures such as indexes, materialized views, source capabilities, access support relations, gmaps, etc. The search space for query plans is de ned and enumerated in a novel manner: the chase phase rewrites the original query into a "universal" plan that integrates all the access structures and alternative pathways that are allowed by applicable constraints. Then, the backchase phase produces optimal plans by eliminating various combinations of redundancies, again according to constraints. This method is applicable (sound) to a large class of queries, physical access structures, and semantic constraints. We prove that it is in fact complete for "path-conjunctive" queries and views with complex objects, classes and dictionaries, going beyond previous theoretical work on processing queries using materialized views.

In a previous paper we proposed a novel method for generating alternative query plans that uses chasing (and back-chasing) with logical constraints. The method brings together use of indexes, use of materialized views, semantic optimization and join elimination (minimization). Each of these techniques is known separately to be beneficial to query optimization. The novelty of our approach is in allowing these techniques to interact systematically, eg. nontrivial use of indexes and materialized views may be enabled only by semantic constraints.

There is already a sizable body of proposals on OODB query optimization. One of the most challenging problems in this area is query unnesting, where the embedded query can take any form, including aggregation and universal quantification. Although there is already a number of proposed techniques for query unnesting, most of these techniques are applicable to only few cases. We believe that the lack of a general and simple solution to the query unnesting problem is due to the lack of a uniform algebra that treats all operations (including aggregation and quantification) in the same way. This paper presents a new query unnesting algorithm that generalizes many unnesting techniques proposed recently in the literature. Our system is capable of removing any form of query nesting using a very simple and efficient algorithm. The simplicity of the system is due to the use of the monoid comprehension calculus as an intermediate form for OODB queries. The monoid comprehension calculus treats op...

This work discusses the CROQUE approach to the maintenance problem for materialized views. In a CROQUE database, application-specified collections (type extents or classes) themselves need not be materialized. In exchange, the system maintains (redundant) views of the application data that help to minimize query response time. We understand views as functions of database objects and examine algebraic properties of these functions, in particular linearity, to derive incremental update plans. It turns out that it is feasible to employ ODMG OQL as a view definition language -- instead of inventing a specialized one -- in such an environment, since the majority of its clauses represent linear functions.

This work tries to employ the monoid comprehension calculus --- which has proven to be an adequate framework to capture the semantics of modern object query languages featuring a family of collection types like sets, bags, and lists --- in a twofold manner: First, serving as a target language for the translation of ODMG OQL queries. We review work done in this field and also give comprehension calculus equivalents for the recently introduced OQL 1.2 concepts. Second, we use monoid comprehensions as the formalism in which we try to find efficient execution methods working on a rich set of physical structures (including indices, vertical and horizontal decomposition, etc.). The main problem coming up here is the "nested-loop nature" of the calculus expressions. While these loop-based semantics for evaluating comprehensions at least provide a way for executing OQL queries, their execution is almost always much less efficient than alternative physical algorithms of the database e...

There is already a sizable body of proposals on OODB query optimization. One of the most challenging problems in this area is query unnesting, where the embedded query can take any form, including aggregation and universal quantification. Even though there is already a number of proposed techniques for query unnesting, these techniques are applicable to few cases only. We believe that the lack of a general and simple solution to the query unnesting problem is caused by the lack of a uniform algebra that treats all operations (including aggregation and quantification) in the same way. This paper presents an OODB optimizer for ODMG OQL, that generalizes and implements the unnesting techniques proposed recently in the literature. It is expressed in an optimizer specification language, OPTL, in the form of a term-rewriting system. Our system is capable of removing any form of query nesting using two rewrite rules only. The simplicity of the system is due to the use of the monoid comprehens...

This paper introduces an algebraic framework for expressing and evaluating queries over XML data. It presents the underlying assumptions of the framework, describes the input and output of the algebraic operators, and defines these operators and their semantics. It evaluates the framework with regard to other proposed XML query algebras. Examples show that this framework is flexible enough to capture queries expressed in Quilt, one of the dominant XML query languages. We have used this algebra in the context of an Internet query engine, in which it is used to formulate logical plans for XML-QL queries. We define equivalence rules that provide opportunities for optimization, and give example cases that point out the usefulness of these rules. 1

Traditionally, query optimizers assume a direct mapping from the logical entities modeling the data (e.g. relations) and the physical entities storing the data (e.g. indexes), each physical entity corresponding precisely to one logical entity. This assumption is no longer true in non-traditional applications (object-oriented and semi-structured databases, data integration), which often exhibit a mismatch between the logical view and the actual storage of data. In addition, there is an increased amount of redundancy, even at the logical level, that can greatly enhance optimization opportunities, if exploited. To deal with all this, we propose a novel architecture for query optimization, in which physical optimization is leveraged at the level of query rewriting. As a consequence, the other important aspect of query optimization, semantic optimization (that takes advantage of the redundancy at the logical level), can be naturally incorporated. The optimizer can then make global decisions based on both semantic and physical knowledge, leading to plans of higher quality than those obtainable by a traditional two-level approach. The main idea

Object-oriented databases (OODBs) provide powerful data abstractions and modeling facilities but they usually lack a suitable framework for query processing and optimization. Even though there is an increasing number of recent proposals on OODB query optimization, only few of them are actually focused on query optimization in the presence of object identity and destructive updates, features often supported by most realistic OODB languages. This paper presents a formal framework for optimizing object-oriented queries in the presence of side effects. These queries may contain object updates at any place and in any form. We present a language extension to the monoid comprehension calculus to express these object-oriented features and we give a formal meaning to these extensions. Our method is based on denotational semantics, which is often used to give a formal meaning to imperative programming languages. The semantics of our language extensions is expressed in terms of our monoid calculu...