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Scheduling problems in transportation networks of line topology

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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

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

References

  1. Adler, M., Khanna, S., Rajaraman, R., Rosen, A.: Time-constrained scheduling of weighted packets on trees and meshes. Algorithmica 36, 123–152 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Adler, M., Rosenberg, A.L., Sitaraman, R.K., Unger, W.: Scheduling time-constrained communication in linear networks. In: Proceedings of 10th ACM Symposium on Parallel Algorithms and Architectures, pp. 269–278 (1998)

  3. Bermond, J.-C., Nisse, N., Reyes, P., Rivano, H.: Minimum delay data gathering in radio networks. Ad-Hoc, Mobile and Wireless Networks, Lecture Notes in Computer Science, vol. 5793, pp. 69–82 (2009)

  4. Klasing, R., Korteweg, P., Stougie, L., Marchetti-Spaccamela, A.: Data gathering in wireless networks. In: Graphs and Algorithms in Communication Networks, Springer Monograph, Springer, Berlin (2009)

  5. Bonifaci, V., Korteweg, P., Marchetti-Spaccamela, A., Stougie, L.: An approximation algorithm for the wireless gathering problem. Oper. Res. Lett. 36(5), 605–608 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Busch, C., Magdon-Ismail, M., Mavronicolas, M., Wattenhofer, R.: Near-Optimal Hot-Potato Routing on Trees. Euro-Par, pp. 820–827 (2004)

  7. Cidon, I., Kutten, S., Mansour, Y., Peleg, D.: Greedy Packet Scheduling. SIAM J. Comput. 24(1), 148–157 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gargano, L.: Time optimal gathering in sensor networks. Proc. Struct. Inform. Commun. Complexity 4474, 7–10 (2007)

    Article  Google Scholar 

  9. Leighton, F.T., Maggs, B.M., Rao, S.B.: Packet routing and job-shop scheduling in O(congestion + dilation) steps. Combinatorica 14(2), 167–180 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Li, C.-L., McCormick, S.T., Simchi-Levi, D.: The complexity of finding two disjoint paths with min-max objective function. Discrete Appl. Math. 26(1), 105–115 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Leighton, F.T., Maggs, B.M., Richa, A.: Fast algorithms for finding O(Congestion + Dilation) packet routing schedules. Combinatorica 19(3), 375–401 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Leung, Y-T, J., Tam, T., Young, G.: On-line routing of real-time messages. J. Parallel Distrib. Comput. 34, 211–217 (1996)

  13. Liu, K.-S., Zaks, S.: Scheduling in synchronous networks and the greedy algorithm. Theor. Comput. Sci. 220(1), 157–183 (1999)

    Article  Google Scholar 

  14. Mansour, Y., Patt-Shamir, B.: Greedy packet scheduling on shortest paths. J. Algorithms 14, 449–465 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ostrovsky, R., Rabani, Y.: Universal \(O\)(congestion + dilation + \(\log ^{1+\varepsilon }N\)) local control packet switching algorithms. In: Proceedings of ACM Symposium on Theory of Computing, pp. 644–653 (1997)

  16. Peis, B., Skutella, M., Wiese, A.: “Packet routing on the grid”, in LATIN 2010. LNCS 6034, 120–130 (2010)

    Google Scholar 

  17. Rabani, Y., Tardos, E.: Distributed packet switching in arbitrary networks. In: Proceedings of ACM Symposium on the Theory of Computing, pp. 366–375 (1996)

  18. Revah, Y., Segal, M.: Improved algorithms for data-gathering time in sensor networks II: ring, tree, and grid Topologies. Int. J. Distri. Sens. Netw. 5, 463–479 (2009)

    Article  Google Scholar 

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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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Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, UK

    Dariusz R. Kowalski

  2. Communication Systems Engineering Department, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Eyal Nussbaum, Michael Segal & Vitaly Milyeykovsky

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  1. Dariusz R. Kowalski
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  2. Eyal Nussbaum
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  3. Michael Segal
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  4. Vitaly Milyeykovsky
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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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  • DOI: https://doi.org/10.1007/s11590-013-0613-x

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