The School Bus Problem on Trees

  • Adrian Bock
  • Elyot Grant
  • Jochen Könemann
  • Laura Sanità
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)


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.


Travelling Salesman Problem Junction Point Capacitate Vehicle Route Problem Euler Tour Core Segment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Adrian Bock
    • 1
  • Elyot Grant
    • 2
  • Jochen Könemann
    • 2
  • Laura Sanità
    • 1
  1. 1.EPFLLausanneSwitzerland
  2. 2.University of WaterlooCanada

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