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Some Results on Node Lifting of TSP Inequalities

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  • Robert Carr

    (Sandia National Labs)

Abstract

We can define important classes of TSP inequalities by performing Naddef and Rinaldi's node lifting operation on simple TSP inequalities. We present some new insights into the node lifting operation, namely that 1-node lifting of cut based inequalities always has a geometric interpretation if a certain claw-free condition which is satisfied by most of these TSP inequalities is met. We go on to show that node lifting of the subtour elimination inequalities does not yield any new inequalities.

Suggested Citation

  • Robert Carr, 2000. "Some Results on Node Lifting of TSP Inequalities," Journal of Combinatorial Optimization, Springer, vol. 4(4), pages 395-414, December.
    • Handle: RePEc:spr:jcomop:v:4:y:2000:i:4:d:10.1023_a:1009830409833
    DOI: 10.1023/A:1009830409833
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    References listed on IDEAS

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    1. Sylvia C. Boyd & William H. Cunningham, 1991. "Small Travelling Salesman Polytopes," Mathematics of Operations Research, INFORMS, vol. 16(2), pages 259-271, May.
    2. M. Padberg & G. Rinaldi, 1989. "A Branch-and-Cut Approach to a Traveling Salesman Problem with Side Constraints," Management Science, INFORMS, vol. 35(11), pages 1393-1412, November.
    3. Robert Carr, 1997. "Separating Clique Trees and Bipartition Inequalities Having a Fixed Number of Handles and Teeth in Polynomial Time," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 257-265, May.
    4. Denis Naddef, 1992. "The Binested Inequalities for the Symmetric Traveling Salesman Polytope," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 882-900, November.
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    Cited by:

    1. Robert Carr, 2004. "Separation Algorithms for Classes of STSP Inequalities Arising from a New STSP Relaxation," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 80-91, February.

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