Karim, M: Straight-Line Grid Drawings of Planar Graphs with Sub-Quadratic Area

A graph is an abstract structure that is used to model information. Many real-world situations can conveniently be described by means of graphs. Smaller area of a drawing increases the readability of the drawing. Compact drawing of a circuit is preferable for VLSI fabrication since a compact drawing helps us to avoid wasting of valuable wafer space. This book deals with area efficient straight-line drawings of planar graphs. We have introduced some classes of planar graphs that admit straight-line grid drawing with sub-quadratic area. We introduce ``doughnut graphs,'' a subclass of 5-connected planar graphs as well as 3-outerplanar graphs, which admits a straight-line grid drawing on a grid of area O(n). We introduce a subclass of 4-connected planar graphs that admits straight-line grid drawing with linear area. We also introduce a subclass of outerplanar graphs, which we call ``label-constrained outerplanar graphs,'' that admits straight-line grid drawings with O(nlog n) area. We give linear-time algorithms to find such drawings. We also give linear-time algorithms for recognition of these classes of graphs.