Abstract
Edge casing is a well-known method to improve the readability of drawings of non-planar graphs. A cased drawing orders the edges of each edge crossing and interrupts the lower edge in an appropriate neighborhood of the crossing. Certain orders will lead to a more readable drawing than others. We formulate several optimization criteria that try to capture the concept of a “good” cased drawing. Further, we address the algorithmic question of how to turn a given drawing into an optimal cased drawing. For many of the resulting optimization problems, we either find polynomial time algorithms or NP-hardness results.
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References
Cabello, S., Haverkort, H., van Kreveld, M., Speckmann, B.: Algorithmic aspects of proportional symbol maps. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 720–731. Springer, Heidelberg (2006)
Chen, R.-W., Kajitani, Y., Chan, S.-P.: A graph-theoretic via minimization algorithm for two-layer printed circuit boards. IEEE Transactions on Circuits and Systems 30(5), 284–299 (1983)
Eppstein, D.: Testing bipartiteness of geometric intersection graphs. In: Proc. 15th ACM-SIAM Symposium on Discrete Algorithms, pp. 853–861. ACM Press, New York (2004)
Even, S., Itai, A., Shamir, A.: On the complexity of timetable and multicommodity flow problems. SIAM Journal on Computing 5(4), 691–703 (1976)
Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for general graph-matching problems. Journal of the ACM 38(4), 815–853 (1991)
Lichtenstein, D.: Planar formulae and their uses. SIAM Journal on Computing 11(2), 329–343 (1982)
Mulmuley, K.: Computational Geometry: An Introduction through Randomized Algorithms. Prentice-Hall, Englewood Cliffs (1994)
Pach, J., Pollack, R., Welzl, E.: Weaving patterns of lines and line segments in space. Algorithmica 9(6), 561–571 (1993)
Venkateswaran, V.: Minimizing maximum indegree. Discrete Applied Mathematics 143, 374–378 (2004)
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Eppstein, D., van Kreveld, M., Mumford, E., Speckmann, B. (2007). Edges and Switches, Tunnels and Bridges. In: Dehne, F., Sack, JR., Zeh, N. (eds) Algorithms and Data Structures. WADS 2007. Lecture Notes in Computer Science, vol 4619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73951-7_8
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DOI: https://doi.org/10.1007/978-3-540-73951-7_8
Publisher Name: Springer, Berlin, Heidelberg
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