A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Facet identification for the symmetric traveling salesman polytope
Mathematical Programming: Series A and B
The graphical relaxation: a new framework for the Symmetric Traveling Salesman Polytope
Mathematical Programming: Series A and B
Worst-case comparison of valid inequalities for the TSP
Mathematical Programming: Series A and B
On the number of small cuts in a graph
Information Processing Letters
Mathematical Programming: Series A and B
Computing All Small Cuts in an Undirected Network
SIAM Journal on Discrete Mathematics
Mathematics of Operations Research
Separating Maximally Violated Comb Inequalities in Planar Graphs
Mathematics of Operations Research
Separating a Superclass of Comb Inequalities in Planar Graphs
Mathematics of Operations Research
Polynomial-Time Separation of Simple Comb Inequalities
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
A study of domino-parity and k-parity constraints for the TSP
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Exploiting planarity in separation routines for the symmetric traveling salesman problem
Discrete Optimization
Fast separation algorithms for three-index assignment problems
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
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The comb inequalities are a well-known class of facet-inducing inequalities for the traveling salesman problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: Either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality one, or both. The simple comb inequalities generalize the classical 2-matching inequalities of Edmonds [Edmonds, J. 1965. Maximum matching and a polyhedron with 0--1 vertices. J. Res. Nat. Bur. Standards69B 125--130] and also the so-called Chvátal comb inequalities. In 1982, Padberg and Rao [Padberg, M. W., M. R. Rao. 1982. Odd minimum cut-sets and b-matchings. Math. Oper. Res.7 67--80] gave a polynomial-time separation algorithm for the 2-matching inequalities, i.e., an algorithm for testing if a given fractional solution to an LP relaxation violates a 2-matching inequality. We extend this significantly by giving a polynomial-time separation algorithm for a class of valid inequalities which includes all simple comb inequalities.