eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-06-04
10:1
10:14
10.4230/LIPIcs.SWAT.2018.10
article
On the Size of Outer-String Representations
Biedl, Therese
1
Biniaz, Ahmad
1
Derka, Martin
2
Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada
School of Computer Science, Carleton University, Ottawa, Canada
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 run-time 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 graphs, 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol101-swat2018/LIPIcs.SWAT.2018.10/LIPIcs.SWAT.2018.10.pdf
string graph
outer-string graph
size of representation
independent set