Polynomial-Time Separation of Simple Comb Inequalities

Polynomial-Time Separation of a Superclass of Simple Comb Inequalities

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...

Polynomial-Time Separation of Simple Comb Inequalities

Separating a Superclass of Comb Inequalities in Planar Graphs

Many classes of valid and facet-inducing inequalities are known for the family of polytopes associated with the Symmetric Travelling Salesman Problem (STSP), including subtour elimination, 2-matching and comb inequalities. For a given class of inequalities, an exact separation algorithm is a procedure which, given an LP relaxation vector x∗, 7nds one or more inequalities in the class which are ...

Separating Simple Domino Parity Inequalities

In IPCO 2002, Letchford and Lodi describe an algorithm for separating simple comb inequalities that runs in O(nm log n) time, where n and m are respectively the number of nodes and arcs in the support graph of the point to be separated. In this extended abstract, we demonstrate that the above algorithm separates over a superclass of simple comb inequalities, which we call simple domino parity i...

On Disjunctive Cuts for Combinatorial Optimization

In the successful branch-and-cut approach to combinatorial optimization, linear inequalities are used as cutting planes within a branch-and-bound framework. Although researchers often prefer to use facet-inducing inequalities as cutting planes, good computational results have recently been obtained using disjunctive cuts, which are not guaranteed to be facet-inducing in general. A partial expla...