Abstract
An ortho-radial grid is described by concentric circles and straight-line spokes emanating from the circles’ center. An ortho-radial drawing is the analog of an orthogonal drawing on an ortho-radial grid. Such a drawing has an unbounded outer face and a central face that contains the origin. Building on the notion of an ortho-radial representation [1], we describe an integer-linear program (ILP) for computing bend-free ortho-radial representations with a given embedding and fixed outer and central face. Using the ILP as a building block, we introduce a pruning technique to compute bend-optimal ortho-radial drawings with a given embedding and a fixed outer face, but freely choosable central face. Our experiments show that, in comparison with orthogonal drawings using the same embedding and the same outer face, the use of ortho-radial drawings reduces the number of bends by \(43.8 \%\) on average. Further, our approach allows us to compute ortho-radial drawings of embedded graphs such as the metro system of Beijing or London within seconds.
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Barth, L., Niedermann, B., Rutter, I., Wolf, M.: Towards a topology-shape-metrics framework for ortho-radial drawings. In: Aronov, B., Katz, M.J. (eds.) Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), vol. 77, pp. 14:1–14:16. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2017)
Biedl, T., Kant, G.: A better heuristic for orthogonal graph drawings. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 24–35. Springer, Heidelberg (1994). https://doi.org/10.1007/BFb0049394
Biedl, T., Kant, G.: A better heuristic for orthogonal graph drawings. Comput. Geom. 9(3), 159–180 (1998)
Bläsius, T., Rutter, I., Wagner, D.: Optimal orthogonal graph drawing with convex bend costs. ACM Trans. Algorithms 12(3), 33 (2016)
Bläsius, T., Lehmann, S., Rutter, I.: Orthogonal graph drawing with inflexible edges. Comput. Geom. 55, 26–40 (2016)
Chimani, M., Gutwenger, C., Jünger, M., Klau, G.W., Klein, K., Mutzel, P.: The open graph drawing framework (OGDF). In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization, pp. 543–569. CRC Press (2013). Chap. 17
Duncan, C.A., Goodrich, M.T.: Planar Orthogonal and Polyline Drawing Algorithms. In: Handbook of Graph Drawing and Visualization, pp. 223–246. CRC Press (2013)
Felsner, S., Kaufmann, M., Valtr, P.: Bend-optimal orthogonal graph drawing in the general position model. Comput. Geom. 47(3, Part B), 460–468 (2014). Special Issue on the 28th European Workshop on Computational Geometry (EuroCG 2012)
Gurobi Optimization, L.: Gurobi optimizer reference manual (2020). http://www.gurobi.com
Hasheminezhad, M., Hashemi, S.M., McKay, B.D., Tahmasbi, M.: Rectangular-radial drawings of cubic plane graphs. Comput. Geom. Theory Appl. 43, 767–780 (2010)
Hasheminezhad, M., Hashemi, S.M., Tahmasbi, M.: Ortho-radial drawings of graphs. Australas. J. Comb. 44, 171–182 (2009)
Niedermann, B., Rutter, I.: An integer-linear program for bend-minimization in ortho-radial drawings. CoRR abs/2008.10373v2 (2013)
Niedermann, B., Rutter, I., Wolf, M.: Efficient algorithms for ortho-radial graph drawing. In: Barequet, G., Wang, Y. (eds.) Proceedings of the 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), vol. 129, pp. 53:1–53:14. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2019)
Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. J. Comput. 16(3), 421–444 (1987)
Wu, H.Y., Niedermann, B., Takahashi, S., Roberts, M.J., Nöllenburg, M.: A survey on transit map layout - from design, machine, and human perspectives. Comput. Graph. Forum 39(3), 619–646 (2020)
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Niedermann, B., Rutter, I. (2020). An Integer-Linear Program for Bend-Minimization in Ortho-Radial Drawings. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_19
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DOI: https://doi.org/10.1007/978-3-030-68766-3_19
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