Separating over classes of TSP inequalities defined by 0 node-lifting in polynomial time
Many important cutting planes nave been discovered for the traveling salesman problem. Until recently (see  and ), little was known in the way of exact algorithms for separating these inequalities in polynomial time in the size of the fractional point x* which is being separated. Any facet-defining inequality can be neatly categorized by the simple inequality which it is a 0 node-lifting of. Given a class of inequalities consisting of simple inequalities occuring on a fixed sized graph together with all their O node-liftings, an algorithm is presented here that separates over this class of inequalities in polynomial time. This algorithm uses a relaxation of the TSP which we will call cycle-shrink. Cycle-shrink is a compact description of the subtour polytope, and has some other theoretically interesting properties.
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