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Planar Graph Drawing

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The book presents the important fundamental theorems and algorithms on planar graph drawing with easy-to-understand and constructive proofs. Extensively illustrated and with exercises included at the end of each chapter, it is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph theory, graph drawing, information visualization and computational geometry. The book will also serve as a useful reference source for researchers in the field of graph drawing and software developers in information visualization, VLSI design and CAD.

This book deals with theories and algorithms for drawing planar graphs. Graph drawing has appeared as a lively area in computer science due to its applications in almost all branches of science and technology. Many researchers have concentrated their attention on drawing planar graphs for the following reasons:
  • drawings of planar graphs have no edge crossings, and look nice;
  • drawings of planar graphs have practical applications in VLSI floorplanning and routing, architectural floorplanning, displaying RNA structures in bioinformatics, etc.; and
  • algorithms for drawing planar graphs can be successfully used for drawing a nonplanar graph by transforming it into a similar planar graph.
During the last two decades numerous results have been published on drawing planar graphs. For example, in 1990 it was shown that every planar graph of n vertices has a straight-line drawing on a grid of area O(n2). This result solved the open question for about four decades whether a planar graph has a straight line drawing on a grid of a polynomial area. Many algorithms have been developed to produce drawings of planar graphs with different styles to fulfill different application needs. While developing these algorithms, many elegant theories on the properties of planar graphs have been discovered, which have applications in solving problems on planar graphs other than graph drawing problems. For example, Schnyder introduced a “realizer” to produce straight line drawings of planar graphs, but later a realizer is used to solve the “independent spanning tree problem” of a certain class of planar graphs. A “canonical ordering” which was introduced by de Fraysseix et al. is later used to solve a “graph partitioning problem.” On the other hand, many established graph theoretic results have been successfully used to solve graph drawing problems. For example, the problem of orthogonal drawings of plane graphs with the minimum number of bends is solved by reducing the problem to a network flow problem.

This book is based on our graph drawing research project supported by Japan Society for the Promotion of Science (JSPS) and Tohoku University. We also acknowledge Bangladesh University of Engineering and Technology (BUET) for providing the second author necessary leave to write this book. We thankfully mention the names of our colleagues Yasuhito Asano and Xiao Zhou at Tohoku university and Md. Shamsul Alam, Mohammad Kaykobad and Md. Abul Kashem Mia at BUET for their encouraging comments on the book. The second author wishes to thank his parents for supporting him throughout his life and for encouraging him to stay in a foreign country for the sake of writing this book.
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