Clustering Cycles into Cycles of Clusters

In this paper we study simple families of clustered graphs that are highly unconnected. We start by studying 3-cluster cycles, which are clustered graphs such that the underlying graph is a simple cycle and there are three clusters all at the same level. We show that in this case, testing the c-planarity can be done efficiently and give an efficient drawing algorithm. Also, we characterize 3-cluster cycles in terms of formal grammars. Finally, we generalize the results on 3-cluster cycles considering clustered graphs that have a cycle structure at each level of the inclusion tree. We present efficient c-planarity testing and drawing algorithms also for this case. Article Type Communicated by Submitted Revised Regular paper E. R. Gansner and J. Pach November 2004 July 2005 Work partially supported by European Commission — Fet Open project DELIS — Dynamically Evolving Large Scale Information Systems — Contract no 001907, by MIUR under Project ALGO-NEXT (Algorithms for the Next Gen...

• Type: Conference
• Year: 2004
• Where: GD
• Authors: Pier Francesco Cortese, Giuseppe Di Battista, Maurizio Patrignani, Maurizio Pizzonia
• Keywords: 3-cluster Cycles, Drawing Algorithms, Efficient Drawing Algorithm, GD 2004