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Approximating the Crossing Number of Dense Graphs (Poster Abstract)

Author Oriol Solé Pi

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ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Approximation algorithms
Keywords
  • Crossing numbers
  • Approximation algorithms
  • Geometric graph theory

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Abstract

We present a deterministic n^(2+o(1))-time algorithm that approximates the crossing number of any graph G of order n up to an additive error of o(n⁴), as well as a randomized polynomial-time algorithm that constructs a drawing of G with cr(G)+o(n⁴) crossings. These results imply a (1+o(1))-approximation algorithm for the crossing number of dense graphs. Our work builds on the machinery used by Fox, Pach and Súk [Fox et al., 2016], who obtained similar results for the rectilinear crossing number.

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Oriol Solé Pi. Approximating the Crossing Number of Dense Graphs (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 54:1-54:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.GD.2024.54

Author Details

Oriol Solé Pi
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

References

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