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Sebastien Roch (sebastien.rochpolymtl.ca) Abstract: 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 tollcompatible shortest paths. We first prove that this problem is strongly NPhard. We then provide a polynomial time algorithm with a worstcase 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. Keywords: network pricing, approximation algorithms, Stackelberg games, combinatorial optimization, NPhard problems Category 1: Combinatorial Optimization Category 2: Network Optimization Citation: Cahiers du GERAD, G200261, HEC Montreal, Montreal, Canada, november 2002. Download: [Postscript][PDF] Entry Submitted: 03/18/2003 Modify/Update this entry  
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