Cuts from Blossoms and Blocks

Comb inequalities have a long history in the TSP, going back to the by-hand computations of Dantzig, Fulkerson, and Johnson [151]. The general comb template is now a workhorse in TSP codes. An important open question, however, is to determine the complexity of the exact separation of comb inequalities, given a vectorx ∗satisfying all subtour constraints. No polynomial-time algorithm is known for the problem, but neither is it known to be${{\mathcal N}{\mathcal P}}$-hard. A practical method for the exact separation of combs would likely have a dramatic impact on our ability to solve large-scale instances of the TSP. The