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Strongly Monotone Drawings of Planar Graphs

Authors Stefan Felsner, Alexander Igamberdiev, Philipp Kindermann, Boris Klemz, Tamara Mchedlidze, Manfred Scheucher

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Stefan Felsner
Alexander Igamberdiev
Philipp Kindermann
Boris Klemz
Tamara Mchedlidze
Manfred Scheucher

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Stefan Felsner, Alexander Igamberdiev, Philipp Kindermann, Boris Klemz, Tamara Mchedlidze, and Manfred Scheucher. Strongly Monotone Drawings of Planar Graphs. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.SoCG.2016.37

Abstract

A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the direction of the line segment connecting the two vertices. We present algorithms to compute crossing-free strongly monotone drawings for some classes of planar graphs; namely, 3-connected planar graphs, outerplanar graphs, and 2-trees. The drawings of 3-connected planar graphs are based on primal-dual circle packings. Our drawings of outerplanar graphs depend on a new algorithm that constructs strongly monotone drawings of trees which are also convex. For irreducible trees, these drawings are strictly convex.
Keywords
  • graph drawing
  • planar graphs
  • strongly monotone
  • strictly convex
  • primal-dual circle packing

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References

  1. Soroush Alamdari, Timothy M. Chan, Elyot Grant, Anna Lubiw, and Vinayak Pathak. Self-approaching graphs. In Walter Didimo and Maurizio Patrignani, editors, Proc. 20th Int. Symp. Graph Drawing (GD'12), volume 7704 of Lecture Notes Comput. Sci., pages 260-271. Springer, 2013. URL: http://dx.doi.org/10.1007/978-3-642-36763-2_23.
  2. Patrizio Angelini, Enrico Colasante, Giuseppe Di Battista, Fabrizio Frati, and Maurizio Patrignani. Monotone drawings of graphs. J. Graph Algorithms Appl., 16(1):5-35, 2012. URL: http://dx.doi.org/10.7155/jgaa.00249.
  3. Patrizio Angelini, Walter Didimo, Stephen Kobourov, Tamara Mchedlidze, Vincenzo Roselli, Antonios Symvonis, and Stephen Wismath. Monotone drawings of graphs with fixed embedding. Algorithmica, 71:1-25, 2013. URL: http://dx.doi.org/10.1007/s00453-013-9790-3.
  4. Esther M. Arkin, Robert Connelly, and Joseph S. B. Mitchell. On monotone paths among obstacles with applications to planning assemblies. In Proc. 5th Ann. ACM Symp. Comput. Geom. (SoCG'89), pages 334-343. ACM, 1989. URL: http://dx.doi.org/10.1145/73833.73870.
  5. Graham R. Brightwell and Edward R. Scheinerman. Representations of planar graphs. SIAM J. Discrete Math., 6(2):214-229, 1993. URL: http://dx.doi.org/10.1137/0406017.
  6. Hooman R. Dehkordi, Fabrizio Frati, and Joachim Gudmundsson. Increasing-chord graphs on point sets. In Christian Duncan and Antonios Symvonis, editors, Proc. 22nd Int. Symp. Graph Drawing (GD'14), volume 8871 of Lecture Notes Comput. Sci., pages 464-475. Springer, 2014. URL: http://dx.doi.org/10.1007/978-3-662-45803-7_39.
  7. Raghavan Dhandapani. Greedy drawings of triangulations. Discrete Comput. Geom., 43(2):375-392, 2010. URL: http://dx.doi.org/10.1007/s00454-009-9235-6.
  8. Stefan Felsner. Convex drawings of planar graphs and the order dimension of 3-polytopes. Order, 18(1):19-37, 2001. URL: http://dx.doi.org/10.1023/A:1010604726900.
  9. Dayu He and Xin He. Nearly optimal monotone drawing of trees. Theoretical Computer Science, 2016. To appear. URL: http://dx.doi.org/10.1016/j.tcs.2016.01.009.
  10. Xin He and Dayu He. Compact monotone drawing of trees. In Dachuan Xu, Donglei Du, and Dingzhu Du, editors, Proc. 21st Int. Conf. Comput. Combin. (COCOON'15), volume 9198 of Lecture Notes Comput. Sci., pages 457-468. Springer, 2015. URL: http://dx.doi.org/10.1007/978-3-319-21398-9_36.
  11. Xin He and Dayu He. Monotone drawings of 3-connected plane graphs. In Nikhil Bansal and Irene Finocchi, editors, Proc. 23rd Ann. Europ. Symp. Algorithms (ESA'15), volume 9294 of Lecture Notes Comput. Sci., pages 729-741. Springer, 2015. URL: http://dx.doi.org/10.1007/978-3-662-48350-3_61.
  12. Md. Iqbal Hossain and Md. Saidur Rahman. Monotone grid drawings of planar graphs. In Jianer Chen, John E. Hopcroft, and Jianxin Wang, editors, Proc. 8th Int. Workshop Front. Algorithmics (FAW'14), volume 8497 of Lecture Notes Comput. Sci., pages 105-116. Springer, 2014. URL: http://dx.doi.org/10.1007/978-3-319-08016-1_10.
  13. Weidong Huang, Peter Eades, and Seok-Hee Hong. A graph reading behavior: Geodesic-path tendency. In Peter Eades, Thomas Ertl, and Han-Wei Shen, editors, Proc. 2nd IEEE Pacific Visualization Symposium (PacificVis'09), pages 137-144. IEEE Computer Society, 2009. URL: http://dx.doi.org/10.1109/PACIFICVIS.2009.4906848.
  14. Christian Icking, Rolf Klein, and Elmar Langetepe. Self-approaching curves. Math. Proc. Camb. Philos. Soc., 125:441-453, 1995. URL: http://dx.doi.org/10.1017/S0305004198003016.
  15. Philipp Kindermann, André Schulz, Joachim Spoerhase, and Alexander Wolff. On monotone drawings of trees. In Christian Duncan and Antonis Symvonis, editors, Proc. 22nd Int. Symp. Graph Drawing (GD'14), volume 8871 of Lecture Notes Comput. Sci., pages 488-500. Springer, 2014. URL: http://dx.doi.org/10.1007/978-3-662-45803-7_41.
  16. Bongshin Lee, Catherine Plaisant, Cynthia Sims Parr, Jean-Daniel Fekete, and Nathalie Henry. Task taxonomy for graph visualization. In Enrico Bertini, Catherine Plaisant, and Giuseppe Santucci, editors, Proc. AVI Workshop Beyond Time Errors: Novel Eval. Methods Inform. Vis. (BELIC'06), pages 1-5. ACM, 2006. URL: http://dx.doi.org/10.1145/1168149.1168168.
  17. Tom Leighton and Ankur Moitra. Some results on greedy embeddings in metric spaces. Discrete Comput. Geom., 44(3):686-705, 2010. URL: http://dx.doi.org/10.1007/s00454-009-9227-6.
  18. Martin Nöllenburg and Roman Prutkin. Euclidean greedy drawings of trees. In Hans L. Bodlaender and Giuseppe F. Italiano, editors, Proc. 21st Europ. Symp. Algorithms (ESA'13), volume 8125 of Lecture Notes Comput. Sci., pages 767-778. Springer, 2013. URL: http://dx.doi.org/10.1007/978-3-642-40450-4_65.
  19. Martin Nöllenburg, Roman Prutkin, and Ignaz Rutter. On self-approaching and increasing-chord drawings of 3-connected planar graphs. J. Comput. Geom., 7(1):47-69, 2016. URL: http://jocg.org/v7n1p3.
  20. Ananth Rao, Sylvia Ratnasamy, Christos H. Papadimitriou, Scott Shenker, and Ion Stoica. Geographic routing without location information. In David B. Johnson, Anthony D. Joseph, and Nitin H. Vaidya, editors, Proc. 9th Ann. Int. Conf. Mob. Comput. Netw. (MOBICOM'03), pages 96-108. ACM, 2003. URL: http://dx.doi.org/10.1145/938985.938996.
  21. Kenneth Stephenson. Introduction to circle packing: the theory of discrete analytic functions. Cambridge Univ. Press, 2005. URL: http://www.cambridge.org/9780521823562.
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