An Approximation Algorithm for Stackelberg Network Pricing

TL;DR

This paper addresses the complex problem of setting tolls in transportation networks to maximize revenue, proving its NP-hardness and providing a polynomial-time approximation algorithm with a proven worst-case guarantee.

Contribution

The authors introduce a novel approximation algorithm for the Stackelberg network pricing problem with a tight worst-case bound, advancing computational methods in network revenue optimization.

Findings

The problem is strongly NP-hard.

A polynomial-time approximation algorithm with a ${1/2} ext{log}_2 m_T+1$ guarantee is developed.

The approximation bound is shown to be tight through constructed instances.

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 ${1/2}\log_2 m_T+1$, 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.