Stack and Queue Layouts of Directed Acyclic Graphs: Part I
SIAM Journal on Computing
On embedding an outer-planar graph in a point set
Computational Geometry: Theory and Applications
Drawing colored graphs on colored points
Theoretical Computer Science
Embeddability Problems for Upward Planar Digraphs
Graph Drawing
Computing upward topological book embeddings of upward planar digraphs
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Upward point-set embeddability
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Upward geometric graph embeddings into point sets
GD'10 Proceedings of the 18th international conference on Graph drawing
On ρ-constrained upward topological book embeddings
GD'09 Proceedings of the 17th international conference on Graph Drawing
Upward point set embeddability for convex point sets is in P
GD'11 Proceedings of the 19th international conference on Graph Drawing
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We study the problem of upward point set embeddability, that is the problem to decide whether an n-vertex directed graph has an upward planar drawing when its vertices have to be placed on the points of a given point set of size n. We first present some positive and negative results concerning directed trees and convex point sets. Next, we prove that upward point set embeddability can be solved in polynomial time for the case of a directed tree and a convex point set. Further, we extend our approach to the class of outerplanar directed graphs. This implies that upward point set embeddability can be efficiently solved for the case of convex point sets. Finally, we show that the general problem of upward point set embeddability is NP-complete even for 2-convex point sets.