Data warehouses were envisioned to facilitate analytical reporting and data visualization by providing a model for the flow of data from operational databases to decision support environments. Decision support environments provide a multidimensional conceptual view of the underlying data warehouse, which is usually stored in relational DBMSs. Typically, there is an impedance mismatch between this conceptual view — shared also by all decision support applications accessing the data warehouse — and the physical model of the data stored in relational DBMSs. This thesis presents a mapping compilation algorithm in the context of the Conceptual Integration Model (CIM) [67] framework. In the CIM framework, the relationships between the conceptual model and the physical model are specified by a set of attribute-to-attribute correspondences. The algorithm compiles these correspondences into a set of mappings that associate each construct in the conceptual model with a query on the physical model. Moreover, the homogeneity and summarizability of data in conceptual models is the key to accurate query answering, a necessity in decision making environments. A data-driven approach to refactor relational models into summarizable schemas and instances is proposed as the solution of this issue. We outline the algorithms and challenges in bridging multidimensional conceptual models and the physical model of data warehouses and discuss experimental results.

In this thesis we consider two classes of binary matroids, even cycle matroids and even cut matroids. They are a generalization of graphic and cographic matroids respectively. We focus on two main problems for these classes of matroids. We first consider the Isomorphism Problem, that is the relation between two representations of the same matroid. A representation of an even cycle matroid is a pair formed by a graph together with a special set of edges of the graph. Such a pair is called a signed graph. A representation for an even cut matroid is a pair formed by a graph together with a special set of vertices of the graph. Such a pair is called a graft. We show that two signed graphs representing the same even cycle matroid relate to two grafts representing the same even cut matroid. We then present two classes of signed graphs and we solve the Isomorphism Problem for these two classes. We conjecture that any two representations of the same even cycle matroid are either in one of these two classes, or are related by a local modification of a known operation, or form a sporadic example. The second problem we consider is finding the excluded minors for these classes of matroids. A difficulty when looking for excluded minors for these classes arises from the fact that in general the matroids may have an arbitrarily large number of representations. We define degenerate even cycle and even cut matroids. We show that a 3-connected even cycle matroid containing a 3-connected non-degenerate minor has, up to a simple equivalence relation, at most twice as many representations as the minor. We strengthen this result for a particular class of non-degenerate even cycle matroids. We also prove analogous results for even cut matroids.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (leaves 48-49).

Thesis (Ph.D.) -- University of Newcastle, 2003. / School of Mathematical and Physical Sciences. Includes bibliographical references (p. 161-162). "Also available online".

Thesis (M.Sc.) - Carleton University, 2005. / Includes bibliographical references (p. 61-63). Also available in electronic format on the Internet.

Thesis (B.A.)--Haverford College, Dept. of Computer Science, 2005. / Includes bibliographical references.

Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 243-245). Also available via the Internet.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2009. / Includes bibliographical references.

Thesis (Ph. D.)--Rutgers University, 2007. / "Graduate Program in Mathematics." Includes bibliographical references (p. 64-65).

Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Mihail, Milena; Committee Member: Lu, Linyuan; Committee Member: Sokol, Joel; Committee Member: Tetali, Prasad; Committee Member: Trotter, Tom; Committee Member: Yu, Xingxing. Part of the SMARTech Electronic Thesis and Dissertation Collection.