Bock, Adrian Aloysius
Grant, Elyot
Könemann, Jochen
Sanità, Laura
The School Bus Problem on Trees
Algorithms And Computation
978-3-642-25590-80302-9743
7074
10-19
10
The School Bus Problem is an NP-hard vehicle routing problem in which the goal is to route buses that transport children to a school such that for each child, the distance travelled on the bus does not exceed the shortest distance from the child's home to the school by more than a given regret threshold. Subject to this constraint and bus capacity limit, the goal is to minimize the number of buses required. In this paper, we give a polynomial time 4-approximation algorithm when the children and school are located at vertices of a fixed tree. As a byproduct of our analysis, we show that the integrality gap of the natural set-cover formulation for this problem is also bounded by 4. We also present a constant approximation for the variant where we have a fixed number of buses to use, and the goal is to minimize the maximum regret.
Network design;
Vehicle Routing;
Approximation algorithms;
Springer-Verlag Berlin
Berlin
2011
http://infoscience.epfl.ch/record/170056/files/sbp-isaac-final.pdf;