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Linear Time Approximation Schemes for Vehicle Scheduling

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Algorithm Theory — SWAT 2002 (SWAT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2368))

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Abstract

We consider makespan minimization for vehicle scheduling problems on trees with release and handling times. 2-approximation algorithms were known for several variants of the single vehicle problem on a path [16]. 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 [13]. Karuno, Nagamochi and Ibaraki give a 2-approximation algorithm for the single vehicle problem on trees. We develop a linear time PTAS for the single vehicle scheduling problem on trees which 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. For this problem, the only previous result is a 2-approximation algorithm for paths [10]. Finally, we present competitive online algorithms for some single vehicle scheduling problems.

This research was partially supported by the Research Competitiveness Subprogram of the Louisiana Board of Regents.

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Author information

Authors and Affiliations

  1. Dept. of Electrical & Computer Eng., Louisiana State University, Baton Rouge, LA, 70803, USA

    John E. Augustine

  2. Department of Computer Science, Louisiana State University, 298 Coates Hall, Baton Rouge, LA, 70803, USA

    Steven S. Seiden

Authors
  1. John E. Augustine
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  2. Steven S. Seiden
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Applied Mathematics, University of Kuopio, P.O. Box 1627, 70211, Kuopio, Finland

    Martti Penttonen

  2. BRICS, University of Aarhus, Department of Computer Science, NY Munkegade, 8000, Aarhus C, Denmark

    Erik Meineche Schmidt

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© 2002 Springer-Verlag Berlin Heidelberg

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Augustine, J.E., Seiden, S.S. (2002). Linear Time Approximation Schemes for Vehicle Scheduling. In: Penttonen, M., Schmidt, E.M. (eds) Algorithm Theory — SWAT 2002. SWAT 2002. Lecture Notes in Computer Science, vol 2368. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45471-3_4

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  • DOI: https://doi.org/10.1007/3-540-45471-3_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43866-3

  • Online ISBN: 978-3-540-45471-7

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