Evaluation of optimization techniques for aggregation

Aggregations are almost always done at the top of operator tree after all selections and joins in a SQL query. But actually they can be done before joins and make later joins much cheaper when used properly. Although some enumeration algorithms considering eager aggregation are proposed, no sufficient evaluations are available to guide the adoption of this technique in practice. And no evaluations are done for real data sets and real queries with estimated cardinalities. That means it is not known how eager aggregation performs in the real world. In this thesis, a new estimation method for group by and join combining traditional estimation method and index-based join sampling is proposed and evaluated. Two enumeration algorithms considering eager aggregation are implemented and compared in the context of estimated cardinality. We find that the new estimation method works well with little overhead and that under certain conditions, eager aggregation can dramatically accelerate queries

A branch-and-bound methodology within algebraic modelling systems

Through the use of application-specific branch-and-bound directives it is possible to find solutions to combinatorial models that would otherwise be difficult or impossible to find by just using generic branch-and-bound techniques within the framework of mathematical programming. {\sc Minto} is an example of a system which offers the possibility to incorporate user-provided directives (written in {\sc C}) to guide the branch-and-bound search. Its main focus, however, remains on mathematical programming models. The aim of this paper is to present a branch-and-bound methodology for particular combinatorial structures to be embedded inside an algebraic modelling language. One advantage is the increased scope of application. Another advantage is that directives are more easily implemented at the modelling level than at the programming level

Ontology-based model abstraction

In recent years, there has been a growth in the use of reference conceptual models to capture information about complex and critical domains. However, as the complexity of domain increases, so does the size and complexity of the models that represent them. Over the years, different techniques for complexity management in large conceptual models have been developed. In particular, several authors have proposed different techniques for model abstraction. In this paper, we leverage on the ontologically well-founded semantics of the modeling language OntoUML to propose a novel approach for model abstraction in conceptual models. We provide a precise definition for a set of Graph-Rewriting rules that can automatically produce much-reduced versions of OntoUML models that concentrate the models’ information content around the ontologically essential types in that domain, i.e., the so-called Kinds. The approach has been implemented using a model-based editor and tested over a repository of OntoUML models

Self-Dual and Complementary Dual Abelian Codes over Galois Rings

Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes over Galois rings are studied in terms of the ideals in the group ring ${\rm GR}(p^r,s)[G]$, where $G$ is a finite abelian group and ${\rm GR}(p^r,s)$ is a Galois ring. Characterizations of self-dual abelian codes have been given together with necessary and sufficient conditions for the existence of a self-dual abelian code in ${\rm GR}(p^r,s)[G]$. A general formula for the number of such self-dual codes is established. In the case where $\gcd(|G|,p)=1$, the number of self-dual abelian codes in ${\rm GR}(p^r,s)[G]$ is completely and explicitly determined. Applying known results on cyclic codes of length $p^a$ over ${\rm GR}(p^2,s)$, an explicit formula for the number of self-dual abelian codes in ${\rm GR}(p^2,s)[G]$ are given, where the Sylow $p$-subgroup of $G$ is cyclic. Subsequently, the characterization and enumeration of complementary dual abelian codes in ${\rm GR}(p^r,s)[G]$ are established. The analogous results for self-dual and complementary dual cyclic codes over Galois rings are therefore obtained as corollaries.Comment: 22 page