Straight-line drawing algorithms for hierarchical graphs and clustered graphs

Abstract

Hierarchical graphs and clustered graphs are useful nonclassical graph models for structured relational ioformation. Hierarchical graphs are graphs with layering structtLres; clustered graphs are graphs with recursive clustering structures. Both have appfications in CASE tools, software visualization, VLSI design, etc. Drawing algorithms for hierarchical graphs have been well investigated. However, the problem of straight-fine representation has not been addressed. In this paper, we answer the question: does every planar hierarchical graph admit a planar straight-line hierarchical drawing? We present ata algorithm that constructs such drawings in O(n2) time. Also, we answer a basic question for clustered graphs, i.e. does every planar clustered graph admit a planar straight-line drawing with clusters drawn as convex polygons? A method for such drawings is provided in this paper.