Area minimization for grid visibility representation of hierarchically planar graphs

Authors:
Xuemin Lin;Peter Eades
Affiliations:
School of Computer Science & Engineering, The University of New South Wales, Sydney, NSW, Australia;Department of Computer Science & Software Engineering, The University of Newcastle, Callaghan, NSW, Australia
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

Hierarchical graphs are an important class of graphs for modelling many real applications in software and information visualization. In this paper, we shall investigate the computational complexity of constructing minimum area grid visibility representations of hierarchically planar graphs. Firstly, we provide a quadratic algorithm that minimizes the drawing area with respect to a fixed planar embedding. This implies that the area minimization problem is polynomial time solvable restricted to the class of graphs whose planar embeddings are unique. Secondly, we show that the area minimization problem is generally NP-hard.