Linear time approximation schemes for vehicle scheduling problems

Authors:
John E. Augustine;Steven Seiden
Affiliations:
444 CS Building, UCI, Irvine CA;Department of Computer Science, LSU, Baton Rouge, LA
Venue:
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
Year:
2004

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Abstract

We consider makespan minimization for vehicle scheduling problems on trees with job requests that have release and handling times. 2-approximation algorithms were known for several variants of the single vehicle problem on a path. A 3/2-approximation algorithm was known for the single vehicle problem on a path where there is a fixed starting point and the vehicle must return to the starting point upon completion. Karuno, Nagamochi and Ibaraki give a 2-approximation algorithm for the single vehicle problem on trees. We develop a polynomial time approximation scheme (PTAS) that runs in time linear in the number of job requests for the single vehicle scheduling problem on trees that have a constant number of leaves. This PTAS can be easily adapted to accommodate various starting/ending constraints. We then extended this to a PTAS for the multiple vehicle problem where vehicles operate in disjoint subtrees.