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Titel:

Recognizing and Drawing IC-Planar Graphs

AutorInnen:

Franz J. Brandenburg
Walter Didimo
William S. Evans
Philipp Kindermann
Giuseppe Liotta
Fabrizio Montecchiani

Kategorie:

Artikel in Zeitschriften

erschienen in:

Theoretical Computer Science, Vol. 636, 2016, pp. 1-16

Abstract:

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph G with n vertices, we present an O(n)-time algorithm that computes a straight-line drawing of G in quadratic area, and an O(n³)-time algorithm that computes a straight-line drawing of G with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar.

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BibTeX-Eintrag:

@Article{bdeklm-rdicp-tcs16, Title = {Recognizing and Drawing IC-Planar Graphs}, Author = {Franz J. Brandenburg and Walter Didimo and William S. Evans and Philipp Kindermann and Giuseppe Liotta and Fabrizio Montecchiani}, Journal = {Theoretical Computer Science}, Year = {2016}, Pages = {1--16}, Volume = {636}, Abstract = {IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$ vertices, we present an $O(n)$-time algorithm that computes a straight-line drawing of $G$ in quadratic area, and an $O(n^3)$-time algorithm that computes a straight-line drawing of $G$ with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar.}, Doi = {10.1016/j.tcs.2016.04.026} }