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Javier Pena (jfpandrew.cmu.edu) Abstract: We study certain linear and semidefinite programming lifting approximation schemes for computing the stability number of a graph. Our work is based on, and refines De Klerk and Pasechnik's approach to approximating the stability number via copositive programming (SIAM J. Optim. 12 (2002), 875892). We provide a closedform expression for the values computed by the linear programming approximations. We also show that the exact value of the stability number $\alpha(G)$ is attained by the semidefinite approximation of order $\alpha(G)1$ as long as $\alpha(G) \leq 6$. Our results reveal some sharp differences between the linear and the semidefinite approximations. For instance, the value of the linear programming approximation of any order is strictly larger than $\alpha(G)$ whenever $\alpha(G) > 1$. Keywords: stability number, copositivity, polynomials, lifting procedures Category 1: Combinatorial Optimization (Other ) Category 2: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: SIAM Journal on Optimization 18 (2007) pp. 87105. Download: Entry Submitted: 04/08/2005 Modify/Update this entry  
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