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The clique problem for graphs with a few eigenvalues of the same sign

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Abstract

The quadratic programming problem is known to be NP-hard for Hessian matrices with only one negative eigenvalue, but it is tractable for convex instances. These facts yield to consider the number of negative eigenvalues as a complexity measure of quadratic programs. We prove here that the clique problem is tractable for two variants of its Motzkin-Strauss quadratic formulation with a fixed number of negative eigenvalues (with multiplicities).

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Acknowledgments

Research is partially supported by LATNA laboratory, National Research University Higher School of Economics, RF government grant, ag. 11.G34.31.00357.

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Authors and Affiliations

  1. National Research University Higher School of Economics, 25/12 Bolshaja Pecherskaja, Ulitsa, Nizhny Novgorod, 603155, Russia

    D. S. Malyshev

  2. University of Florida, 401 Weil Hall, P.O. Box 116595, Gainesville, FL, 326116595, USA

    P. M. Pardalos

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  1. D. S. Malyshev
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  2. P. M. Pardalos
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Correspondence to D. S. Malyshev.

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Malyshev, D.S., Pardalos, P.M. The clique problem for graphs with a few eigenvalues of the same sign. Optim Lett 9, 839–843 (2015). https://doi.org/10.1007/s11590-014-0805-z

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  • DOI: https://doi.org/10.1007/s11590-014-0805-z

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