Gene Ontology information related to the biological role of genes is organized in a hierarchical manner that can be represented by a directed acyclic graph (DAG). Space filling visualizations, such as the treemaps, have the capacity to display thousands of items legibly in limited space via a two-dimensional rectangular map. Treemaps have been used to visualize the Gene Ontology by first transforming the DAG into a tree. However this transformation has several undesirable effects such as producing trees with a large number of nodes and scattering the rectangles associated with the duplicates of a node around the display rectangle. In this paper we introduce the problem of visualizing a DAG with space filling techniques without converting it to a tree first, we present two special cases of the problem, and we discuss complexity issues.
Gene Ontology information related to the biological role of genes is organized in a hierarchical manner that can be represented by a directed acyclic graph (DAG). Treemaps graphically represent hierarchical information via a two-dimensional rectangular map. They efficiently display large trees in limited screen space. Treemaps have been used to visualize the Gene Ontology by first transforming the DAG into a tree. However this transformation has several undesirable effects such as producing trees with a large number of nodes and scattering the rectangles associated with the duplicates of a node around the screen. In this paper we introduce the problem of visualizing a DAG as a treemap, we present two special cases, and we discuss complexity results.
The development of the Semantic Web proceeds in steps, building each layer on top of the other. Currently, the focus of research efforts is concentrated on logic and proofs, both of which are essential, since they will allow systems to infer new knowledge by applying principles on the existing data and explain their actions. Research is shifting towards the study of non-monotonic systems that are capable of handling conflicts among rules and reasoning with partial information. As for the proof layer of the Semantic Web, it can play a vital role in increasing the reliability of Semantic Web systems, since it will be possible to provide explanations and/or justifications of the derived answers. This paper reports on the implementation of a system for visualizing proof explanations on the Semantic Web. The proposed system applies defeasible logic, a member of the non-monotonic logics family, as the underlying inference system. The proof representation schema is based on a graph-based methodology for visualizing defeasible logic rule bases.
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