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Optimization Letters

, Volume 9, Issue 5, pp 839–843 | Cite as

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

  • D. S. MalyshevEmail author
  • P. M. Pardalos
Original Paper

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).

Keywords

Quadratic programming Computational complexity Clique problem 

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsUlitsaRussia
  2. 2.University of FloridaGainesvilleUSA

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