# Computing with Domino-Parity Inequalities for the Traveling Salesman Problem (TSP)

@article{Cook2007ComputingWD, title={Computing with Domino-Parity Inequalities for the Traveling Salesman Problem (TSP)}, author={William J. Cook and Daniel G. Espinoza and Marcos Goycoolea}, journal={INFORMS J. Comput.}, year={2007}, volume={19}, pages={356-365} }

We describe methods for implementing separation algorithms for domino-parity inequalities for the symmetric traveling salesman problem. These inequalities were introduced by Letchford (2000), who showed that the separation problem can be solved in polynomial time when the support graph of the LP solution is planar. In our study we deal with the problem of how to use this algorithm in the general (nonplanar) case, continuing the work of Boyd et al. (2001). Our implementation includes pruning…

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## References

SHOWING 1-10 OF 28 REFERENCES

Separating Maximally Violated Comb Inequalities in Planar Graphs

- Computer ScienceIPCO
- 1996

This paper considers the problem of finding violated comb inequalities in a fractional solution in the subtour elimination polytope whose graph is planar, and proposes an algorithm that runs in O(n + MC(n)) time, whereMC(n) is the time to compute all minimum cuts of a planar graph.

A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems

- Computer ScienceSIAM Rev.
- 1991

An algorithm is described for solving large-scale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality. The core of the algorithm is a “polyhedral” cutting-plane procedure that…

Exploiting planarity in separation routines for the symmetric traveling salesman problem

- BusinessDiscret. Optim.
- 2008

The domino inequalities: facets for the symmetric traveling salesman polytope

- MathematicsMath. Program.
- 2003

It is shown in [5] that one does not lose any facet inducing inequality restricting the Domino Parity inequalities to Domino inequalities, except maybe for some very particular case.

On the domino-parity inequalities for the STSP

- Computer ScienceMath. Program.
- 2007

This work presents several performance enhancements for this separation routine for the STSP within a branch and cut framework, and discusses the implementation of this improved algorithm.

Separating a Superclass of Comb Inequalities in Planar Graphs

- Mathematics, Computer ScienceMath. Oper. Res.
- 2000

Ageneralization of comb inequalities is defined and it is shown that the associated separation problem can be solved efficiently when the subgraph induced by the edges withx*e>0 is planar.

Edmonds polytopes and weakly hamiltonian graphs

- MathematicsMath. Program.
- 1973

A direct application of the linear programming duality theorem leads to a new necessary condition for the existence of hamiltonian circuits; this condition appears to be stronger than the ones previously known.

On the symmetric travelling salesman problem I: Inequalities

- MathematicsMath. Program.
- 1979

It is proved that all subtour-elimination and all comb inequalities define facets of the symmetric travelling salesman polytope.

Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems

- Computer ScienceMath. Program.
- 2003

An implementation of Dantzig et al.'s method is discussed that is suitable for TSP instances having 1,000,000 or more cities, and used as a step towards understanding the applicability and limits of the general cutting-plane method in large-scale applications.

Polynomial-Time Separation of a Superclass of Simple Comb Inequalities

- MathematicsMath. Oper. Res.
- 2006

This work gives a polynomial-time separation algorithm for a class of valid inequalities which includes all simple comb inequalities, which generalize the classical 2-matching inequalities of Edmonds and Chvatal.