Decomposition theorem on matchable distributive lattices

A distributive lattice structure ${\mathbf M}(G)$ has been established on the set of perfect matchings of a plane bipartite graph $G$. We call a lattice {\em matchable distributive lattice} (simply MDL) if it is isomorphic to such a distributive lattice. It is natural to ask which lattices are MDLs. We show that if a plane bipartite graph $G$ is elementary, then ${\mathbf M}(G)$ is irreducible. Based on this result, a decomposition theorem on MDLs is obtained: a finite distributive lattice $\mathbf{L}$ is an MDL if and only if each factor in any cartesian product decomposition of $\mathbf{L}$ is an MDL. Two types of MDLs are presented: $J(\mathbf{m}\times \mathbf{n})$ and $J(\mathbf{T})$, where $\mathbf{m}\times \mathbf{n}$ denotes the cartesian product between $m$-element chain and $n$-element chain, and $\mathbf{T}$ is a poset implied by any orientation of a tree.Comment: 19 pages, 7 figure

Analyzing Mappings and Properties in Data Warehouse Integration

The information inside the Data Warehouse (DW) is used to take strategic decisions inside the organization that is why data quality plays a crucial role in guaranteeing the correctness of the decisions. Data quality also becomes a major issue when integrating information from two or more heterogeneous DWs. In the present paper, we perform extensive analysis of a mapping-based DW integration methodology and of its properties. In particular, we will prove that the proposed methodology guarantees coherency, meanwhile in certain cases it is able to maintain soundness and consistency. Moreover, intra-schema homogeneity is discussed and analysed as a necessary condition for summarizability and for optimization by materializing views of dependent queries