ISI:000308788400003
Bock, Adrian Aloysius
Grant, Elyot
Könemann, Jochen
Sanità, Laura
The School Bus Problem on Trees
Berlin, Springer-Verlag Berlin
http://infoscience.epfl.ch/record/170056/files/sbp-isaac-final.pdf
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.
2011-11-10T09:07:29Z
http://infoscience.epfl.ch/record/170056
http://infoscience.epfl.ch/record/170056
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