IPCO 2008 Summer School University Residential Center, Bertinoro (Forlì-Cesena), Italy May 29-30, 2008 The IPCO Summer School will take place immediately after the IPCO conference. The lecturers will be Michele Conforti, Franz Rendl and Martin Skutella. Lectures' program Michele Conforti Extended Formulations in Integer Programming and Combinatorial Optimization An extended formulation of a polyhedron P is a system of inequalties S that defines a polyhedron Q in a higher dimensional space such that P is the projection of Q in the original space. If one can efficiently optimize a linear function over Q then one can optimize it over P, and if S is a "small" system, optimizing over Q can be efficiently done via Linear Programming. We first discuss a result of Yannakakis on the existence of such small systems and then survey some extended formulations in Combinatorial Optimization, related to matchings, cuts, stable sets, hamiltonian tours, etc. Extended formulati...
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