# Worst-case comparison of valid inequalities for the TSP

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## 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## Preview

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© The Mathematical Programming Society, Inc. 1995