کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
431144 | 688282 | 2008 | 22 صفحه PDF | دانلود رایگان |
In this paper we consider the problem of finding three-dimensional orthogonal drawings of maximum degree six graphs from the computational complexity perspective. We introduce a 3SAT reduction framework that can be used to prove the NP-hardness of finding three-dimensional orthogonal drawings with specific constraints. By using the framework we show that, given a three-dimensional orthogonal shape of a graph (a description of the sequence of axis-parallel segments of each edge), finding the coordinates for nodes and bends such that the drawing has no intersection is NP-complete. Conversely, we show that if node coordinates are fixed, finding a shape for the edges that is compatible with a non-intersecting drawing is a feasible problem, which becomes NP-complete if a maximum of two bends per edge is allowed. We comment on the impact of these results on the two open problems of determining whether a graph always admits a drawing with at most two bends per edge and of characterizing orthogonal shapes admitting an orthogonal drawing without intersections.
Journal: Journal of Discrete Algorithms - Volume 6, Issue 1, March 2008, Pages 140–161