Planarity of Additively Drawn Concept Lattices

In Formal Concept Analysis, it is a very important but quite difficult task to draw line diagrams of concept lattices automatically. In particular, we want every planar lattice to be visualized without edge crossings. Many algorithms ignore that fact or find plane diagrams only heuristically. We present a characterization of planar lattices based on the theorem of Baker, Fishburn and Roberts [1] and the "left"-relation introduced by Rival [5]. In particular, our work is helpful for drawing attribute- (or dually object-) additive diagrams. 1 Motivation There exist algorithms for embedding lattices into the plane already, see [2] for an overview. These algorithms do not use the lattice structure, but more general ones (graphs or acyclic digraphs) for the characterisation of planar lattices. We want to use the convention of attribute-additively drawn diagrams [3], because it provides nice visualizations of lattices. By applying this rule, the coordinates of the nodes of the attr...

• Type: Conference
• Year: 2004
• Where: CLA
• Authors: Christian Zschalig
• Keywords: CLA 2004, CLA 2007, Concept Lattices, Formal Concept Analysis, Planar Lattices