Area requirements for drawing hierarchically planar graphs [chapter]

Xuemin Lin, Peter Eades
1997 Lecture Notes in Computer Science  
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 visibifity 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
more » ... 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 visibifity drawing algoiithm which is efficient and guarantees the minimum drawing area.
doi:10.1007/3-540-63938-1_64 fatcat:vqxhepwm2bec5p2vamstciax4u