Home | Issues | About JGAA | Instructions for Authors |
DOI: 10.7155/jgaa.00165
C-Planarity of C-Connected Clustered Graphs
Pier Francesco Cortese,
Giuseppe Di Battista,
Fabrizio Frati,
Maurizio Patrignani, and
Maurizio Pizzonia
Vol. 12, no. 2, pp. 225-262, 2008. Regular paper.
Abstract We present the first characterization of c-planarity for
c-connected clustered graphs. The characterization is based on the
interplay between the hierarchy of the clusters and the hierarchies of
the triconnected and biconnected components of the underlying graph.
Based on such a characterization, we provide a
linear-time c-planarity testing and embedding algorithm for
c-connected clustered graphs. The algorithm is reasonably easy to
implement, since it exploits as building blocks simple algorithmic
tools like the computation of lowest common ancestors, minimum
and maximum spanning trees, and counting sorts. It also makes use
of well-known data structures as SPQR-trees and BC-trees. If the test fails,
the algorithm identifies a structural element responsible for the non-c-planarity
of the input clustered graph.
|
Submitted: August 2006.
Accepted: August 2008.
Final: August 2008.
Published: October 2008.
Communicated by
Michael T. Goodrich
|
Journal Supporters
|