Volume Requirements of 3D Upward Drawings
Di Giacomo, Emilio and Liotta, Giuseppe and Meijer, Henk and Wismath, Stephen, K. (2006) Volume Requirements of 3D Upward Drawings. In: Graph Drawing 13th International Symposium, GD 2005, September 12-14, 2005, Limerick, Ireland , pp. 101-110 (Official URL: http://dx.doi.org/10.1007/11618058_10).
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This paper studies the problem of drawing directed acyclic graphs in three dimensions in the straight-line grid model, and so that all directed edges are oriented in a common (upward) direction. We show that there exists a family of outerplanar directed acyclic graphs whose volume requirement is super-linear. We also prove that for the special case of rooted trees a linear volume upper bound is achievable .
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