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On the Complexity of Testing Hypermetric, Negative Type, k-Gonal and Gap Inequalities

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Discrete and Computational Geometry (JCDCG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2866))

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Abstract

Hypermetric inequalities have many applications, most recently in the approximate solution of max-cut problems by linear and semidefinite programming. However, not much is known about the separation problem for these inequalities. Previously Avis and Grishukhin showed that certain special cases of the separation problem for hypermetric inequalities are NP-hard, as evidence that the separation problem is itself hard. In this paper we show that similar results hold for inequalities of negative type, even though the separation problem for negative type inequalities is well known to be solvable in polynomial time. We also show similar results hold for the more general k-gonal and gap inequalities.

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References

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Author information

Authors and Affiliations

  1. Computer Science, Mcgill University and GERAD, 3480 University, Montreal, Quebec, Canada, H3A 2A7

    David Avis

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  1. David Avis
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku Tokio, Japan

    Jin Akiyama

  2. Ibaraki University, Nakanarusawa, Hitachi, 316-8511, Ibaraki, Japan

    Mikio Kano

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Avis, D. (2003). On the Complexity of Testing Hypermetric, Negative Type, k-Gonal and Gap Inequalities. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_6

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  • DOI: https://doi.org/10.1007/978-3-540-44400-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20776-4

  • Online ISBN: 978-3-540-44400-8

  • eBook Packages: Springer Book Archive

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