On Linear Characterizations of Combinatorial Optimization Problems
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We show that there can be no computationally tractable description by linear inequalities of the polyhedron associated with any NP-complete combinatorial optimization problem unless NP = co-NP—a very unlikely event. We also apply the ellipsoid method for linear programming to show that a combinatorial optimization problem is solvable in polynomial time if and only if it admits a small generator of violated inequalities.