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Scheduling problems in transportation networks of line topology

Abstract

In this paper we consider online scheduling problems for linear topology under various objective functions: minimizing the maximum completion time, minimizing the largest delay, and minimizing the sum of completion times. We give optimal solutions for uni-directional version of the problem for each of the objectives and show that for the two-directional versions of each problem, no online algorithm can deterministically achieve the optimal solution for any of the considered objective functions. We also propose 2-approximation on-line algorithms for the MinMakespan and the MinSum minimization objectives. We also prove that no online algorithm can deterministically achieve the optimal solution for any of the considered objective functions for the weighted case of uni-directional scenarios.

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Notes

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    As we will see later, our solutions will use limited size buffers at each node.

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Acknowledgments

We thank anonymous reviewers whose comments significantly improved the presentation of the paper. Work on this paper was partially supported by the Engineering and Physical Sciences Research Council (Grant Numbers EP/G023018/1, EP/H018816/1], US Air Force European Office of Aerospace Research and Development, grant FA8655-09-1-3016, Deutsche Telecom, France Telecom, European project FLAVIA and Israeli Ministry of Industry, Trade and Labor (consortium CORNET).

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Correspondence to Michael Segal.

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Kowalski, D.R., Nussbaum, E., Segal, M. et al. Scheduling problems in transportation networks of line topology. Optim Lett 8, 777–799 (2014). https://doi.org/10.1007/s11590-013-0613-x

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Keywords

  • Scheduling
  • Linear network
  • Online algorithms