Polynomial-Time Separation of Simple Comb Inequalities
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
Exploiting planarity in separation routines for the symmetric traveling salesman problem
Discrete Optimization
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The Traveling Salesman Problem (TSP) is a benchmark problem in combinatorial optimization. It was one of the very first problems used for developing and testing approaches to solving large integer programs, including cutting plane algorithms and branch-and-cut algorithms. Much of the research in this area has been focused on finding new classes of facets for the TSP polytope, and much less attention has been paid to algorithms for separating from these classes of facets. In this paper, we consider the problem of finding violated comb inequalities. If there are no violated subtour constraints in a fractional solution of the TSP, a comb inequality may not be violated by more than 1. Given a fractional solution in the subtour elimination polytope whose graph is planar, we either find a violated comb inequality or determine that there are no comb inequalities violated by 1. Our algorithm runs in O(n + MC(n)) time, where MC(n) is the time to compute a cactus representation of all minimum cuts of a weighted planar graph on n vertices.