Clustering Cycles into Cycles of Clusters (Extended Abstract)
Cortese, Pier Francesco and Di Battista, Giuseppe and Patrignani, Maurizio and Pizzonia, Maurizio (2004) Clustering Cycles into Cycles of Clusters (Extended Abstract). In: Graph Drawing 12th International Symposium, GD 2004, September 29-October 2, 2004, New York, NY, USA , pp. 100-110 (Official URL: http://dx.doi.org/10.1007/978-3-540-31843-9_12).
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In this paper we study the clustered graphs whose underlying graph is a cycle. This is a simple family of clustered graphs that are "highly non connected". We start by studying 3-cluster cycles, that 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 at each level of the inclusion tree have a cycle structure. Even in this case we show efficient c-planarity testing and drawing algorithms. Work partially supported by European Commission – Fet Open project COSIN – COevolution and Self-organisation In dynamical Networks – IST-2001-33555, by European Commission – Fet Open project DELIS – Dynamically Evolving Large Scale Information Systems – Contract no 001907, by ldquoProgetto ALINWEB: Algoritmica per Internet e per il Webrdquo, MIUR Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale, and by ldquoThe Multichannel Adaptive Information Systems (MAIS) Projectrdquo, MIUR–FIRB.
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