Abstract
We generalize the reduction mechanism between linear programming problems from [1] 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 SparsestCut problem, the BalancedSeparator problem, the MaxCut problem and the Matching problem on 3-regular graphs. We also provide a new, very strong Lasserre integrality gap for the IndependentSet problem, which is strictly greater than the best known LP approximation, showing that the Lasserre hierarchy does not always provide the tightest SDP relaxation.
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Acknowledgements
Research reported in this paper was partially supported by NSF CAREER award CMMI-1452463. 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, as well as Levent Tunçel for helpful discussions on Lasserre relaxations of the IndependentSet problem.
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Braun, G., Pokutta, S., Roy, A. (2016). Strong Reductions for Extended Formulations. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_29
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