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Maximizing Ink in Partial Edge Drawings of k-plane Graphs

  • Matthias Hummel
  • Fabian Klute
  • Soeren Nickel
  • Martin NöllenburgEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11904)

Abstract

Partial edge drawing (PED) is a drawing style for non-planar graphs, in which edges are drawn only partially as pairs of opposing stubs on the respective end-vertices. In a PED, by erasing the central parts of edges, all edge crossings and the resulting visual clutter are hidden in the undrawn parts of the edges. In symmetric partial edge drawings (SPEDs), the two stubs of each edge are required to have the same length. It is known that maximizing the ink (or the total stub length) when transforming a straight-line graph drawing with crossings into a SPED is tractable for 2-plane input drawings, but \(\mathsf {NP}\)-hard for unrestricted inputs. We show that the problem remains \(\mathsf {NP}\)-hard even for 3-plane input drawings and establish \(\mathsf {NP}\)-hardness of ink maximization for PEDs of 4-plane graphs. Yet, for k-plane input drawings whose edge intersection graph forms a collection of trees or, more generally, whose intersection graph has bounded treewidth, we present efficient algorithms for computing maximum-ink PEDs and SPEDs. We implemented the treewidth-based algorithms and show a brief experimental evaluation.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Algorithms and Complexity GroupTU WienViennaAustria

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