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Area requirements for drawing hierarchically planar graphs

  • Xuemin Lin
  • Peter Eades
Crossings and Planarity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1353)

Abstract

In this paper, we investigate area requirements for drawing s-t hierarchically planar graphs by straight-lines. Two drawing standards will be discussed: 1) each vertex is represented by a point and 2) grid visibility representation (that is, a line segment is allowed to represent a vertex). For the first drawing standard, we show an exponential area lower bound needed for drawing hierarchically planar graphs. The lower bound holds even for hierarchical graphs without transitive arcs, in contrast to the results for upward planar drawing. Applications of some existing algorithms from upward drawing can guarantee the quadratic drawing area for grid visibility representation but do not necessarily guarantee the minimum drawing area. Motivated by this, we will present another grid visibility drawing algorithm which is efficient and guarantees the minimum drawing area.

Keywords

Graph Drawing Hierarchically Planar Graph Straight Line Drawing Visibility Representation Drawing Area 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Xuemin Lin
    • 1
  • Peter Eades
    • 2
  1. 1.Department of Computer ScienceThe University of Western AustraliaNedlandsAustralia
  2. 2.Department of Computer ScienceThe University of NewcastleCallaghanAustralia

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