Upward Book Embeddings of st-Graphs

03/19/2019 ∙ by Carla Binucci, et al. ∙ 0

We study k-page upward book embeddings (kUBEs) of st-graphs, that is, book embeddings of single-source single-sink directed acyclic graphs on k pages with the additional requirement that the vertices of the graph appear in a topological ordering along the spine of the book. We show that testing whether a graph admits a kUBE is NP-complete for k≥ 3. A hardness result for this problem was previously known only for k = 6 [Heath and Pemmaraju, 1999]. Motivated by this negative result, we focus our attention on k=2. On the algorithmic side, we present polynomial-time algorithms for testing the existence of 2UBEs of planar st-graphs with branchwidth β and of plane st-graphs whose faces have a special structure. These algorithms run in O(f(β)· n+n^3) time and O(n) time, respectively, where f is a singly-exponential function on β. Moreover, on the combinatorial side, we present two notable families of plane st-graphs that always admit an embedding-preserving 2UBE.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.