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. © 2011 Springer-Verlag.
CITATION STYLE
Bock, A., Grant, E., Könemann, J., & Sanità, L. (2011). The school bus problem on trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7074 LNCS, pp. 10–19). https://doi.org/10.1007/978-3-642-25591-5_3
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