In the Stackelberg Network Pricing problem, one has to assign tariffs to a certain subset of the arcs of a given transportation network. The aim is to maximize the amount paid by the user of the network, knowing that the user will take a shortest st-path once the tariffs are fixed. Roch, Savard, and Marcotte (Networks, Vol. 46(1), 57-67, 2005) proved that this problem is NP-hard, and gave an O(log m)-approximation algorithm, where m denote the number of arcs to be priced. In this note, we show that the problem is also APX-hard.
@article{arxiv.0812.0320,
title = {Stackelberg Network Pricing is Hard to Approximate},
author = {Gwenaël Joret},
journal= {arXiv preprint arXiv:0812.0320},
year = {2011}
}