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Discrete & Computational Geometry
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arXiv.org e-Print Archive
Preprint . 2012
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Discrete & Computational Geometry
Article . 2012 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2012
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Discrete & Computational Geometry
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Hardness of Approximation for Crossing Number

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 19 Jul 2012Embargo end date: 01 Jan 2012 English Publisher:Springer Science and Business Media LLCJournal:Discrete & Computational Geometry, volume 49, pages 348-358 (issn: 0179-5376, eissn: 1432-0444, Copyright policy )
Authors: Sergio Cabello;

doi: 10.1007/s00454-012-9440-6 , 10.48550/arxiv.1204.0660

arXiv: http://arxiv.org/abs/1204.0660

Hardness of Approximation for Crossing Number

Abstract

We show that, if P\not=NP, there is a constant c > 1 such that there is no c-approximation algorithm for the crossing number, even when restricted to 3-regular graphs.

10 pages, 4 figures

Related Organizations
Keywords

Computational Geometry (cs.CG), FOS: Computer and information sciences, Computer Science - Computational Complexity, FOS: Mathematics, Computer Science - Computational Geometry, Mathematics - Combinatorics, Combinatorics (math.CO), Computational Complexity (cs.CC)

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    		 18
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
18
Average
Top 10%
Top 10%
Green
bronze
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