Planarity-preserving clustering and embedding for large planar graphs

Authors:
Christian A. Duncan;Michael T. Goodrich;Stephen G. Kobourov
Affiliations:
Department of Computer Science, University of Miami;Department of Information and Computer Science, University of California-Irvine;Department of Computer Science, University of Arizona
Venue:
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Year:
2003

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Abstract

In this paper we present a novel approach for cluster-based drawing of large planar graphs that maintains planarity. Our technique works for arbitrary planar graphs and produces a clustering which satisfies the conditions for compound-planarity (c-planarity). Using the clustering, we obtain a representation of the graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. At the same time, the difference between two graphs on neighboring layers of the hierarchy is small, thus preserving the viewer's mental map. The overall running time of the algorithm is O(n log n), where n is the number of vertices of graph G.