We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly NP-hard. We then provide a polynomial time algorithm with a worst-case precision guarantee of $\frac{1}{2}\log m_T+1$, where $m_T$ denotes the number of toll arcs. Finally we show that the approximation is tight with respect to a natural relaxation by constructing a family of instances for which the relaxation gap is reached.

## Citation

Cahiers du GERAD, G-2002-61, HEC Montreal, Montreal, Canada, november 2002.

## Article

View Design and analysis of an approximation algorithm for Stackelberg network pricing