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Lift-and-project ranks and antiblocker duality

Laszlo Liptak (liptak***at***oakland.edu)
Levent Tuncel (ltuncel***at***math.uwaterloo.ca)

Abstract: Recently, Aguilera et al.\ exposed a beautiful relationship between antiblocker duality and the lift-and-project operator proposed by Balas et al. We present a very short proof of their result that the \BCC-rank of the clique polytope is invariant under complementation. The proof of Aguilera et al. relies on their main technical result, which describes a stronger duality property of all intermediate relaxations. We provide a short proof of this result, too, using simpler and more general arguments. As a result, our theorems are slightly more general. We conclude by proving that such properties do not extend to the $N_0$ and $N$ procedures of Lov\'asz and Schrijver, or to the $N_+$ procedure unless $\cP = \cNP$.

Keywords: stable set problem, antiblocker duality,lift-and-project, semidefinite lifting,integer programming, perfect graphs

Category 1: Combinatorial Optimization

Citation: Research Report CORR 2003-16, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, July 2003

Download: [Postscript]

Entry Submitted: 07/12/2003
Entry Accepted: 07/12/2003
Entry Last Modified: 07/22/2003

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