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On the Size of Outer-String Representations

Authors Therese Biedl, Ahmad Biniaz, Martin Derka

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Graph theory
Keywords
  • string graph
  • outer-string graph
  • size of representation
  • independent set

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Abstract

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.

Cite As Get BibTex

Therese Biedl, Ahmad Biniaz, and Martin Derka. On the Size of Outer-String Representations. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.SWAT.2018.10

Author Details

Therese Biedl
  • Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada
Ahmad Biniaz
  • Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada
Martin Derka
  • School of Computer Science, Carleton University, Ottawa, Canada

Funding

  • Biedl, Therese: Supported by NSERC.
  • Biniaz, Ahmad: Supported by NSERC Postdoctoral Fellowship.
  • Derka, Martin: Supported by NSERC Vanier fellowship while author was a student at University of Waterloo.

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