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Strong reductions for extended formulations

  • Gábor Braun
  • Sebastian Pokutta
  • Aurko Roy
Full Length Paper Series B
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Abstract

We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from Braun et al. (Inapproximability of combinatorial problems via small LPs and SDPs, 2015) in two ways (1) relaxing the requirement of affineness, and (2) extending to fractional optimization problems. As applications we provide several new LP-hardness and SDP-hardness results, e.g., for the Open image in new window problem, the Open image in new window problem, and the Open image in new window problem and show how to extend ad-hoc reductions between Sherali–Adams relaxations to reductions between LPs.

Keywords

Extended formulation Reductions Max cut Sparsest cuts One free bit 

Mathematics Subject Classification

68Q17 90C05 

Notes

Acknowledgements

Parts of this research was conducted at the CMO-BIRS 2015 workshop Modern Techniques in Discrete Optimization: Mathematics, Algorithms and Applications and we would like to thank the organizers for providing a stimulating research environment.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  1. 1.ISyEGeorgia Institute of TechnologyAtlantaUSA
  2. 2.College of ComputingGeorgia Institute of TechnologyAtlantaUSA

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