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Mathematical Programming

, Volume 69, Issue 1–3, pp 335–349 | Cite as

Worst-case comparison of valid inequalities for the TSP

  • Michel X. Goemans
Article

Abstract

We consider most of the known classes of valid inequalities for the graphical travelling salesman polyhedron and compute the worst-case improvement resulting from their addition to the subtour polyhedron. For example, we show that the comb inequalities cannot improve the subtour bound by a factor greater than 10/9. The corresponding factor for the class of clique tree inequalities is 8/7, while it is 4/3 for the path configuration inequalities.

Keywords

Polyhedral combinatorics Valid inequalities Travelling salesman Worst-case analysis 

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Copyright information

© The Mathematical Programming Society, Inc. 1995

Authors and Affiliations

  • Michel X. Goemans
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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