Fair and Efficient Investment in Public Transportation
Organizations: School of Engineering Mathematics and Technology, University of Bristol, Bristol, UK · School of Engineering, Northwestern University, Evanston, USA · School of Computation, Information and Technology, Technical University of Munich, Munich, Germany
Abstract
We study a stylized model of infrastructure investment in public transportation. In our model, each agent travels between a pair of terminals in a network captured by a weighted graph, where edge weights represent distances. The central planner can reduce the travel time along a fixed number of edges, with the goal of maximizing the utilitarian or egalitarian welfare. When there is only one agent, we provide a polynomial-time algorithm that combines Dijkstra's algorithm with a dynamic program. We then demonstrate how to use this algorithm as a subroutine to solve the problem for two agents. Generalizing this idea, we present an XP algorithm parameterized by the number of agents ; however, our problem turns out to be W[1]-hard with respect to . Nevertheless, we establish a fixed-parameter tractability result for the special case where all agents travel to a common hub. If the number of agents is variable, we obtain NP-completeness and inapproximability results. We discuss implications of our results for a related model of railway network design.
Figures & tables
| Problem | Results | Reference | Restrictions |
| 1- | solvable in | Theorem 4.2 | |
| 2- | solvable in | Theorem 4.4 | |
| - | solvable in | Theorem 4.7 | |
| - | solvable in | Theorem 4.11 | |
| - TIP -Dec | -complete | Theorem 4.13 | |
| W[1]-hard param. by number of agents and budget | Theorem 4.9 |
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.