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2010

Convex drawings of hierarchical planar graphs and clustered planar graphs

9 years 10 months ago
Convex drawings of hierarchical planar graphs and clustered planar graphs
: Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI design, CASE tools, software visualisation and visualisation of social networks and biological networks. Straight-line drawing algorithms for hierarchical graphs and clustered graphs have been presented in [P. Eades, Q. Feng, X. Lin and H. Nagamochi, Straight-line drawing algorithms for hierarchical graphs and clustered graphs, Algorithmica, 44, pp. 1-32, 2006]. A straight-line drawing is called a convex drawing if every facial cycle is drawn as a convex polygon. In this paper, it is proved that every internally triconnected hierarchical plane graph with the outer facial cycle drawn as a convex polygon admits a convex drawing. We present an algorithm which constructs such a drawing. We then extend our results to convex representations of clustered planar graphs. It is proved that every internally triconnected clustered plane graph w...
Seok-Hee Hong, Hiroshi Nagamochi
Added 28 Jan 2011
Updated 28 Jan 2011
Type Journal
Year 2010
Where JDA
Authors Seok-Hee Hong, Hiroshi Nagamochi
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