Home  Issues  Aims and Scope  Instructions for Authors 
DOI: 10.7155/jgaa.00355
Point Set Embedding in 3D
Henk Meijer and
Stephen Wismath
Vol. 19, no. 1, pp. 243257, 2015. Concise paper.
Abstract Given a graph G with n vertices and m edges, and a set P of n points on a threedimensional integer grid, the 3D PointSet Embeddability problem is to determine a (threedimensional) crossingfree drawing of G with vertices located at P and with edges drawn as polylines with bendpoints at integer grid points. We solve a variant of the problem in which the points of P lie on a plane. The resulting drawing lies in a bounding box of reasonable volume and uses at most O(logm) bends per edge. If a particular pointset P is not specified, we show that the graph G can be drawn crossingfree with at most O(logm) bends per edge in a volume bounded by O((n+m) logm). Our construction is asymptotically similar to previously known drawings, however avoids a possibly nonpolynomial preprocessing step.

Submitted: July 2013.
Reviewed: April 2015.
Accepted: April 2015.
Final: April 2015.
Published: May 2015.
Communicated by
Prosenjit K. Bose
