Simultaneous graph embedding with bends and circular arcs

Authors:
Justin Cappos;Alejandro Estrella-Balderrama;J. Joseph Fowler;Stephen G. Kobourov
Affiliations:
Department of Computer Science, University of Arizona, 1040 E. Fourth St., Tucson, AZ 85721, USA;Department of Computer Science, University of Arizona, 1040 E. Fourth St., Tucson, AZ 85721, USA;Department of Computer Science, University of Arizona, 1040 E. Fourth St., Tucson, AZ 85721, USA;Department of Computer Science, University of Arizona, 1040 E. Fourth St., Tucson, AZ 85721, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2009

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Abstract

A simultaneous embedding of two vertex-labeled planar graphs on n vertices is possible if there exists a labeled point set of size n such that each of the graphs can be realized on that point set without crossings. We demonstrate how to simultaneously embed a path and an n-level planar graph and how to use radial embeddings for curvilinear simultaneous embeddings of a path and an outerplanar graph. We also show how to use star-shaped levels to find 2-bends per path edge simultaneous embeddings of a path and an outerplanar graph. All embedding algorithms run in O(n) time.