Drawing Graphs in Euler Diagrams

Mutton, Paul and Rodgers, Peter and Flower, Jean (2004) Drawing Graphs in Euler Diagrams. In: Blackwell, Alan and Marriot, Kim and Shimojima, Atsushi, eds. Diagrammatic Representation and Inference. LNAI 2980, Volume. Springer-Verlag pp. 66-81. ISBN 3-540-21268-X. (Full text available)

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http://dx.doi.org/10.1007/b95854

Abstract

We describe a method for drawing graph-enhanced Euler diagrams using a three stage method. The first stage is to lay out the underlying Euler diagram using a multicriteria optimizing system. The second stage is to find suitable locations for nodes in the zones of the Euler diagram using a force based method. The third stage is to minimize edge crossings and total edge length by swapping the location of nodes that are in the same zone with a multicriteria hill climbing method. We show a working version of the software that draws spider diagrams. Spider diagrams represent logical expressions by superimpos-ing graphs upon an Euler diagram. This application requires an extra step in the drawing process because the embedded graphs only convey information about the connectedness of nodes and so a spanning tree must be chosen for each maximally connected component. Similar notations to Euler diagrams enhanced with graphs are common in many applications and our method is generalizable to drawing Hypergraphs represented in the subset standard, or to drawing Hi-graphs where edges are restricted to connecting with only atomic nodes.

Item Type: Conference or workshop item (UNSPECIFIED)
Uncontrolled keywords: Graph Drawing, Euler Diagram, Hypergraph
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Faculties > Science Technology and Medical Studies > School of Computing > Applied and Interdisciplinary Informatics Group
Depositing User: Peter Rodgers
Date Deposited: 24 Nov 2008 18:02
Last Modified: 27 Sep 2012 13:27
Resource URI: http://kar.kent.ac.uk/id/eprint/14206 (The current URI for this page, for reference purposes)
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