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Parameterised Partially-Predrawn Crossing Number

Authors Thekla Hamm , Petr Hliněný



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Author Details

Thekla Hamm
  • Algorithms and Complexity Group, TU Wien, Austria
Petr Hliněný
  • Faculty of Informatics, Masaryk University, Brno, Czech Republic

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Thekla Hamm and Petr Hliněný. Parameterised Partially-Predrawn Crossing Number. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 46:1-46:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.SoCG.2022.46

Abstract

Inspired by the increasingly popular research on extending partial graph drawings, we propose a new perspective on the traditional and arguably most important geometric graph parameter, the crossing number. Specifically, we define the partially predrawn crossing number to be the smallest number of crossings in any drawing of a graph, part of which is prescribed on the input (not counting the prescribed crossings). Our main result - an FPT-algorithm to compute the partially predrawn crossing number - combines advanced ideas from research on the classical crossing number and so called partial planarity in a very natural but intricate way. Not only do our techniques generalise the known FPT-algorithm by Grohe for computing the standard crossing number, they also allow us to substantially improve a number of recent parameterised results for various drawing extension problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Computational geometry
Keywords
  • Crossing Number
  • Drawing Extension
  • Partial Planarity
  • Parameterised Complexity

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References

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