Integer and combinatorial optimization
Integer and combinatorial optimization
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Decomposition and optimization over cycles in binary matroids
Journal of Combinatorial Theory Series B
Facet identification for the symmetric traveling salesman polytope
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
The traveling salesman problem in graphs with some excluded minors
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
Finding Cuts in the TSP (A preliminary report)
Finding Cuts in the TSP (A preliminary report)
Polynomial-Time Separation of a Superclass of Simple Comb Inequalities
Mathematics of Operations Research
Exploiting planarity in separation routines for the symmetric traveling salesman problem
Discrete 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, and also the so-called Chv谩tal comb inequalities.In 1982, Padberg and Rao [29] gave a polynomial-time algorithm for separating the 2-matching inequalities - i.e., 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 algorithm for separating the simple comb inequalities. The key is a result due to Caprara and Fischetti.