Abstract
Any upward drawing D(P) on a two-dimensional integer grid I, of an ordered set P, has completion ¯P with an upward drawing D(¯P) on a two-dimensional integer grid Ī such that the total edge length of D(¯P) does not exceed the total edge length of D(P). Moreover, by (possibly) translating vertices, there is an upward drawing D(P) on I such that Ī=I.
Thus, any integer grid embedding of a two-dimensional ordered set can be extended to a planar upward drawing of its completion, on the same integer grid, without increasing the total edge length.
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© 1995 Springer-Verlag Berlin Heidelberg
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Jourdan, GV., Rival, I., Zaguia, N. (1995). Upward drawing on the plane grid using less ink. In: Tamassia, R., Tollis, I.G. (eds) Graph Drawing. GD 1994. Lecture Notes in Computer Science, vol 894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58950-3_387
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DOI: https://doi.org/10.1007/3-540-58950-3_387
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