TY - GEN
T1 - The school bus problem on trees
AU - Bock, Adrian
AU - Grant, Elyot
AU - Könemann, Jochen
AU - Sanità, Laura
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84055200209&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-25591-5_3
DO - 10.1007/978-3-642-25591-5_3
M3 - Conference contribution
AN - SCOPUS:84055200209
SN - 9783642255908
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 10
EP - 19
BT - Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
T2 - 22nd International Symposium on Algorithms and Computation, ISAAC 2011
Y2 - 5 December 2011 through 8 December 2011
ER -