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Carla Michini (michinidis.uniroma1.it) Abstract: The edge formulation of the stable set problem is defined by twovariable constraints, one for each edge of a graph G, expressing the simple condition that two adjacent nodes cannot belong to a stable set. We study the fractional stable set polytope, i.e. the polytope defined by the linear relaxation of the edge formulation. Even if this polytope is a weak approximation of the stable set polytope, its simple geometrical structure provides deep theoretical insight as well as interesting algorithmic opportunities. Exploiting a graphic characterization of the bases, we first redefine simplex pivots in terms of simple graphic operations, that turn a given basis into an adjacent one. These results lead us to prove that the Hirsch Conjecture is true for the fractional stable set polytope, i.e. the combinatorial diameter of this fractional polytope is at most equal to the number of edges of the given graph. Keywords: stable set, edge formulation, diameter Category 1: Combinatorial Optimization (Polyhedra ) Category 2: Network Optimization Citation: Sapienza University of Rome, June 2012 Download: Entry Submitted: 06/08/2012 Modify/Update this entry  
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