Abstract
We introduce a new model that we call slanted orthogonal graph drawing. While in traditional orthogonal drawings each edge is made of axis-aligned line-segments, in slanted orthogonal drawings intermediate diagonal segments on the edges are also permitted, which allows for: (a) smoothening the bends of the produced drawing (as they are replaced by pairs of “half-bends”), and, (b) emphasizing the crossings of the drawing (as they always appear at the intersection of two diagonal segments). We present an approach to compute bend-optimal slanted orthogonal representations, an efficient heuristic to compute close-to-optimal drawings in terms of the total number of bends using quadratic area, and a corresponding LP formulation, when insisting on bend optimality. On the negative side, we show that bend-optimal slanted orthogonal drawings may require exponential area.
Part of the research was conducted in the framework of ESF project 10-EuroGIGA-OP-003 GraDR “Graph Drawings and Representations”. The work of M.A. Bekos is implemented within the framework of the Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Social Fund (ESF) and the Greek State.
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Keywords
- Planarized Graph
- Linear Program Formulation
- European Social Fund
- Planar Drawing
- Orthogonal Representation
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References
Biedl, T.C., 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)
Cornelsen, S., Karrenbauer, A.: Accelerated bend minimization. Journal of Graph Algorithms Applications 16(3), 635–650 (2012)
Fößmeier, U., Heß, C., Kaufmann, M.: On improving orthogonal drawings: The 4M-algorithm. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 125–137. Springer, Heidelberg (1999)
Fößmeier, U., Kaufmann, M.: Drawing high degree graphs with low bend numbers. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 254–266. Springer, Heidelberg (1996)
Garg, A., Tamassia, R.: On the computational complexity of upward and rectilinear planarity testing. SIAM Journal of Computing 31(2), 601–625 (2001)
Leiserson, C.E.: Area-efficient graph layouts (for VLSI). In: 21st Symposium on Foundations of Computer Science, vol. 1547, pp. 270–281. IEEE (1980)
Nöllenburg, M., Wolff, A.: Drawing and labeling high-quality metro maps by mixed-integer programming. IEEE Trans. Vis. Comput. Graph. 17(5), 626–641 (2011)
Tamassia, R.: On embedding a graph in the grid with the minimum number of bends. SIAM Journal of Computing 16(3), 421–444 (1987)
Tamassia, R., Tollis, I.G.: Planar grid embedding in linear time. IEEE Transactions on Circuits and Systems 36(9), 1230–1234 (1989)
Valiant, L.G.: Universality considerations in VLSI circuits. IEEE Transaction on Computers 30(2), 135–140 (1981)
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Bekos, M.A., Kaufmann, M., Krug, R., Näher, S., Roselli, V. (2013). Slanted Orthogonal Drawings. In: Wismath, S., Wolff, A. (eds) Graph Drawing. GD 2013. Lecture Notes in Computer Science, vol 8242. Springer, Cham. https://doi.org/10.1007/978-3-319-03841-4_37
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DOI: https://doi.org/10.1007/978-3-319-03841-4_37
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