License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2019.13
URN: urn:nbn:de:0030-drops-104170
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10417/
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Binucci, Carla ; Da Lozzo, Giordano ; Di Giacomo, Emilio ; Didimo, Walter ; Mchedlidze, Tamara ; Patrignani, Maurizio

Upward Book Embeddings of st-Graphs

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LIPIcs-SoCG-2019-13.pdf (1 MB)

Abstract

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 b and of plane st-graphs whose faces have a special structure. These algorithms run in O(f(b)* n+n^3) time and O(n) time, respectively, where f is a singly-exponential function on b. Moreover, on the combinatorial side, we present two notable families of plane st-graphs that always admit an embedding-preserving 2UBE.

BibTeX - Entry

@InProceedings{binucci_et_al:LIPIcs:2019:10417,
  author =	{Carla Binucci and Giordano Da Lozzo and Emilio Di Giacomo and Walter Didimo and Tamara Mchedlidze and Maurizio Patrignani},
  title =	{{Upward Book Embeddings of st-Graphs}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Gill Barequet and Yusu Wang},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10417},
  URN =		{urn:nbn:de:0030-drops-104170},
  doi =		{10.4230/LIPIcs.SoCG.2019.13},
  annote =	{Keywords: Upward Book Embeddings, st-Graphs, SPQR-trees, Branchwidth, Sphere-cut Decomposition}
}

Keywords: Upward Book Embeddings, st-Graphs, SPQR-trees, Branchwidth, Sphere-cut Decomposition
Collection: 35th International Symposium on Computational Geometry (SoCG 2019)
Issue Date: 2019
Date of publication: 11.06.2019

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