In this paper, we continue our study of the class of diagram groups. Simply speaking, a diagram is a labelled plane graph bounded by a pair of paths (the top path and the bottom path). To multiply two diagrams, one simply identifies the top path of one diagram with the bottom path of the other diagram, and removes pairs of “reducible” cells. Each diagram group is determined by an alphabet X, co...

We study the Hausdorff Voronoi diagram of a set S of polygonal objects in the plane, a generalization of Voronoi diagrams based on the maximum distance of a point from a polygon, and show that it is equivalent to the Voronoi diagram of S under the Hausdorff distance function. We investigate the structural and combinatorial properties of the Hausdorff Voronoi diagram and give a divide and conque...

Given a point set the Voronoi diagram associates to each point all the locations in a plane that are closer to it . This diagram is often used in spatial analysis to divide an area among points. In the ordinary Voronoi diagram the points are treated as equals and the division is done in a purely geometrical way. A weighted Voronoi diagram is defined as an extension of the original diagram. The ...

This paper presents one proposal for teaching the foundations of object oriented programming using the Unified Modeling Language (UML) as one modeling language and Java as one object oriented programming language. Unlike other approaches where only two types of UML diagrams are used with the intention of transferring them to a codification (class diagram and sequence diagram, or class diagram a...

Bankwitz characterized an alternating diagram representing the trivial knot. A non-alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize an almost alternaing diagram representing the trivial knot. As a corollary we determine an unknotting number one alternating knot with a property that the unknotting operation can be done on its ...

We propose a construction of a global phase diagram for the quantum Hall effect. This global phase diagram is based on our previous constructions of visibility diagrams in the context of the Quantum Hall Effect. The topology of the phase diagram we obtain is in good agreement with experimental observations (when the spin effect can be neglected). This phase diagram does not show floating.

A diagram is the artifact used to show a graphical view of one or more elements of a model. Sometime designer whish to have slightly different views of the same model element: to show variation points, to explore alternatives, to highlight some details, to add stereotypes or comments ... In actual tools, each view is shown in its own diagram, realized by copying a based diagram and adding the m...

The field of diagram recognition faces many challenges, including the great diversity in diagrammatic notations, and the presence of noise and ambiguity during the recognition process. To help address these problems, research is needed into methods for acquiring, representing, and exploiting notational conventions. We review several frameworks for diagram recognition: blackboard systems, schema...

Euler diagrams are a natural method of representing set-theoretic data and have been employed in diverse areas such as visualizing statistical data, as a basis for diagrammatic logics and for displaying the results of database search queries. For effective use of Euler diagrams in practical computer based applications, the generation of a diagram as a set of curves from an abstract description ...

This paper outlines the ongoing work on the realization of a flexible inheritance mechanism for Activity Diagrams that assures the maintenance of syntactical correctness for the derived Activity Diagrams. The objective is to support the reuse of process models especially by applying Activity Diagram inheritance as a variability mechanism in the context of product line oriented software developm...