Polynomial-Time Separation of Simple Comb Inequalities
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
A New Approach to Cactus Construction Applied to TSP Support Graphs
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
TSP Cuts Which Do Not Conform to the Template Paradigm
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Polynomial-Time Separation of a Superclass of Simple Comb Inequalities
Mathematics of Operations Research
Good triangulations yield good tours
Computers and Operations Research
Generalized Domino-Parity Inequalities for the Symmetric Traveling Salesman Problem
Mathematics of Operations Research
Generalized Domino-Parity Inequalities for the Symmetric Traveling Salesman Problem
Mathematics of Operations Research
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
Certification of an optimal TSP tour through 85,900 cities
Operations Research Letters
Exploiting planarity in separation routines for the symmetric traveling salesman problem
Discrete Optimization
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Many classes of valid and facet-inducing inequalities are known for the family of polytopes associated with theSymmetric Travelling Salesman Problem (STSP), includingsubtour elimination, 2-matching andcomb inequalities. For a given class of inequalities, anexact separation algorithm is a procedure which, given an LP relaxation vectorx*, finds one or more inequalities in the class which are violated byx*, or proves that none exist. Such algorithms are at the core of the highly successfulbranch-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.Apartial answer to the comb problem is provided in this paper. We define ageneralization of comb inequalities and show that the associated separation problem can be solved efficiently when the subgraph induced by the edges withx*e0 is planar. The separation algorithm runs in O( n3) time, wheren is the number of vertices in the graph.