Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 2000 |
---|---|

<mark>Journal</mark> | Mathematics of Operations Research |

Issue number | 3 |

Volume | 25 |

Number of pages | 12 |

Pages (from-to) | 443-454 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

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*, finds one or more inequalities in the class which are violated by x*, or proves that none exist. Such algorithms are at the core of the highly successful branch-and-cut algorithms for the STSP. However, whereas polynomial time exact separation algorithms are known for subtour elimination and 2-matching inequalities, the complexity of comb separation is unknown.
A partial answer to the comb problem is provided in this paper. We define a generalization of comb inequalities and show that the associated separation problem can be solved efficiently when the subgraph induced by the edges with x*_e > 0 is planar. The separation algorithm runs in O(n^3) time, where n is the number of vertices in the graph.