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Drawing graphs in euler diagrams
Paul Mutton, Peter Rodgers, and Jean Flower
In Alan Blackwell, Kim Marriot, and Atsushi Shimojima, editors, Diagrams 2004, LNAI 2980, pages 182-196. Springer-Verlag, March 2004.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.
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@inproceedings{1855,
author = {Paul Mutton and Peter Rodgers and Jean Flower},
title = {Drawing Graphs in Euler Diagrams},
month = {March},
year = {2004},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {},
doi = {},
url = {http://www.cs.kent.ac.uk/pubs/2004/1855},
publication_type = {inproceedings},
submission_id = {7338_1080316891},
ISBN = {3-540-21268-X},
booktitle = {Diagrams 2004},
editor = {Alan Blackwell and Kim Marriot and Atsushi Shimojima},
series = {LNAI 2980},
publisher = {Springer-Verlag},
refereed = {yes},
}