Optimization Online


Design and analysis of an approximation algorithm for Stackelberg network pricing

Sebastien Roch (sebastien.roch***at***polymtl.ca)
Patrice Marcotte (marcotte***at***iro.umontreal.ca)
Gilles Savard (gilles***at***crt.umontreal.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 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.

Keywords: network pricing, approximation algorithms, Stackelberg games, combinatorial optimization, NP-hard problems

Category 1: Combinatorial Optimization

Category 2: Network Optimization

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

Download: [Postscript][PDF]

Entry Submitted: 03/18/2003
Entry Accepted: 03/18/2003
Entry Last Modified: 03/18/2003

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society