Abstract
In this paper we produce orthogonal drawings of triconnected planar graphs where a planar embedding is given. Kant presented an algorithm to compute a small orthogonal drawing in linear time. In this paper, we will show that his algorithm in fact produces less bends than the bound shown. Moreover, with a small variation of the algorithm, the number of bends can be reduced even further, which also leads to lower bounds on the grid-size. Both bounds are optimal.
We also present a theorem that gives a bound on the grid-size of an orthogonal drawing, assuming that a bound on the number of bends is known. With the help of this theorem, we can prove bounds on the grid-size for the algorithm of Tamassia, which produces the minimum number of bends. No such bounds were known before.
Some of these results were part of a diploma thesis written at TU Berlin. The author also wants to thank Goos Kant for useful discussions.
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References
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© 1996 Springer-Verlag Berlin Heidelberg
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Biedl, T.C. (1996). Optimal orthogonal drawings of triconnected plane graphs. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_143
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DOI: https://doi.org/10.1007/3-540-61422-2_143
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