Abstract
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.
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Bock, A., Grant, E., Könemann, J., Sanità, L. (2011). The School Bus Problem on Trees. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_3
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DOI: https://doi.org/10.1007/978-3-642-25591-5_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25590-8
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