%0 Generic
%A Patrignani, Maurizio
%D 2006
%E Healy, Patrick
%E Nikolov, Nikola S.
%F gdea_3:705
%I Springer
%P 368-379
%T Complexity Results for Three-dimensional Orthogonal Graph Drawing
%U http://gdea.informatik.uni-koeln.de/705/
%X We introduce the 3SAT reduction framework which can be used to prove the NP-hardness of finding three-dimensional orthogonal drawings with specific constraints. We use it to show that finding a drawing of a graph whose edges have a fixed shape is NP-hard. Also, it is NP-hard finding a drawing of a graph with nodes at prescribed positions when a maximum of two bends per edge is allowed. We comment the impact of these results on the two open problems of determining whether a graph always admits a 3D orthogonal drawing with at most two bends per edge and of characterizing orthogonal shapes admitting a drawing without intersections.