Beyond Planar Graphs

1. Front Matter

   Pages i-viii

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2. Beyond Planar Graphs: Introduction

   • Seok-Hee Hong

   Pages 1-9

3. Quantitative Restrictions on Crossing Patterns

   • Csaba D. Tóth

   Pages 11-29

4. Quasi-planar Graphs

   • Eyal Ackerman

   Pages 31-45

5. 1-Planar Graphs

   • Yusuke Suzuki

   Pages 47-68

6. Algorithms for 1-Planar Graphs

   • Seok-Hee Hong

   Pages 69-87

7. Edge Partitions and Visibility Representations of 1-planar Graphs

   • Giuseppe Liotta, Fabrizio Montecchiani

   Pages 89-107

8. \(\textit{\textbf{k}}\)-Planar Graphs

   • Michael A. Bekos

   Pages 109-130

9. Fan-Planar Graphs

   • Michael A. Bekos, Luca Grilli

   Pages 131-148

10. Right Angle Crossing Drawings of Graphs

    • Walter Didimo

    Pages 149-169

11. Angular Resolutions: Around Vertices and Crossings

    • Yoshio Okamoto

    Pages 171-186

12. Crossing Layout in Non-planar Graph Drawings

    • Martin Nöllenburg

    Pages 187-209

13. Beyond Clustered Planar Graphs

    • Patrizio Angelini, Giordano Da Lozzo

    Pages 211-235

14. Simultaneous Embedding

    • Ignaz Rutter

    Pages 237-265

15. Back Matter

    Pages 267-270

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This book is the first general and extensive review on the algorithmics and mathematical results of beyond planar graphs. Most real-world data sets are relational and can be modelled as graphs consisting of vertices and edges. Planar graphs are fundamental for both graph theory and graph algorithms and are extensively studied. Structural properties and fundamental algorithms for planar graphs have been discovered. However, most real-world graphs, such as social networks and biological networks, are non-planar. To analyze and visualize such real-world networks, it is necessary to solve fundamental mathematical and algorithmic research questions on sparse non-planar graphs, called beyond planar graphs.This book is based on the National Institute of Informatics (NII) Shonan Meeting on algorithmics on beyond planar graphs held in Japan in November, 2016. The book consists of 13 chapters that represent recent advances in various areas of beyond planar graph research. The main aims and objectives of this book include 1) to timely provide a state-of-the-art survey and a bibliography on beyond planar graphs; 2) to set the research agenda on beyond planar graphs by identifying fundamental research questions and new research directions; and 3) to foster cross-disciplinary research collaboration between computer science (graph drawing and computational geometry) and mathematics (graph theory and combinatorics).

New algorithms for beyond planar graphs will be in high demand by practitioners in various application domains to solve complex visualization problems. This book therefore will be a valuable resource for researchers in graph theory, algorithms, and theoretical computer science, and will stimulate further deep scientific investigations into many areas of beyond planar graphs.

• Graph Algorithm
• Graph Drawing
• Computational Geometry
• Graph Theory
• Combinatorial Optimization

• School of Computer Science, University of Sydney, Sydney, Australia

  Seok-Hee Hong

• School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

  Takeshi Tokuyama

Seok-Hee Hong is a professor in the School of Computer Science at the University of Sydney. She has been a member of the ARC College of Experts, an ARC future fellow, a Humboldt fellow, an ARC research fellow, and a project leader of the VALACON (Visualisation and Analysis of Large and Complex Networks) project at NICTA (National ICT Australia). Her main research interests include graph drawing, algorithms, information visualisation and visual analytics.

Takeshi Tokuyama is a professor in the School of Science and Engineering at Kwansei Gakuin University. Previously, he worked for the IBM Tokyo Research Laboratory and Tohoku University. His main research interest is theoretical computer science with its applications. He is a fellow of IPSJ (Information Society of Japan) and IEICE (Institute of Electronics, Information and Communication Engineers) and a senior member of the Academic Council of Japan.​

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