On the Size of Outer-String Representations

Therese Biedl, Ahmad Biniaz, Martin Derka, Marc Herbstritt
2018 Scandinavian Workshop on Algorithm Theory  
Outer-string graphs, i.e., graphs that can be represented as intersection of curves in 2D, all of which end in the outer-face, have recently received much interest, especially since it was shown that the independent set problem can be solved efficiently in such graphs. However, the runtime for the independent set problem depends on N , the number of segments in an outer-string representation, rather than the number n of vertices of the graph. In this paper, we argue that for some outer-string
more » ... aphs, N must be exponential in n. We also study some special string graphs, viz. monotone string graphs, and argue that for them N can be assumed to be polynomial in n. Finally we give an algorithm for independent set in so-called strip-grounded monotone outer-string graphs that is polynomial in n.
doi:10.4230/lipics.swat.2018.10 dblp:conf/swat/BiedlBD18 fatcat:phzzwx3ohbdl7loiwpiucfipxq