Scheduling Maintenance Jobs in Networks

  • Fidaa Abed
  • Lin Chen
  • Yann Disser
  • Martin Groß
  • Nicole Megow
  • Julie Meißner
  • Alexander T. Richter
  • Roman Rischke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10236)

Abstract

We investigate the problem of scheduling the maintenance of edges in a network, motivated by the goal of minimizing outages in transportation or telecommunication networks. We focus on maintaining connectivity between two nodes over time; for the special case of path networks, this is related to the problem of minimizing the busy time of machines.

We show that the problem can be solved in polynomial time in arbitrary networks if preemption is allowed. If preemption is restricted to integral time points, the problem is NP-hard and in the non-preemptive case we give strong non-approximability results. Furthermore, we give tight bounds on the power of preemption, that is, the maximum ratio of the values of non-preemptive and preemptive optimal solutions.

Interestingly, the preemptive and the non-preemptive problem can be solved efficiently on paths, whereas we show that mixing both leads to a weakly NP-hard problem that allows for a simple 2-approximation.

Keywords

Scheduling Maintenance Connectivity Complexity theory Approximation algorithm 

References

  1. 1.
    Bley, A., Karch, D., D’Andreagiovanni, F.: WDM fiber replacement scheduling. Electron. Notes Discret. Math. 41, 189–196 (2013). http://www.sciencedirect.com/science/article/pii/S1571065313000954 CrossRefGoogle Scholar
  2. 2.
    Boland, N., Kalinowski, T., Kaur, S.: Scheduling arc shut downs in a network to maximize flow over time with a bounded number of jobs per time period. J. Comb. Optim. 32(3), 885–905 (2016)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Boland, N., Kalinowski, T., Kaur, S.: Scheduling network maintenance jobs with release dates and deadlines to maximize total flow over time: Bounds and solution strategies. Comput. Oper. Res. 64, 113–129 (2015). http://www.sciencedirect.com/science/article/pii/S0305054815001288 MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Boland, N., Kalinowski, T., Waterer, H., Zheng, L.: Scheduling arc maintenance jobs in a network to maximize total flow over time. Discret. Appl. Math. 163, 34–52 (2014). http://dx.doi.org/10.1016/j.dam.2012.05.027 MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Boland, N.L., Savelsbergh, M.W.P.: Optimizing the hunter valley coal chain. In: Gurnani, H., Mehrotra, A., Ray, S. (eds.) Supply Chain Disruptions: Theory and Practice of Managing Risk, pp. 275–302. Springer, London (2012). doi:10.1007/978-0-85729-778-5_10 CrossRefGoogle Scholar
  6. 6.
    Canetti, R., Irani, S.: Bounding the power of preemption in randomized scheduling. SIAM J. Comput. 27(4), 993–1015 (1998). http://dx.doi.org/10.1137/S0097539795283292 MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Chang, J., Khuller, S., Mukherjee, K.: LP rounding and combinatorial algorithms for minimizing active and busy time. In: Blelloch, G.E., Sanders, P. (eds.) Proceedings of the 26th SPAA, pp. 118–127. ACM, New York (2014). http://doi.acm.org/10.1145/2612669.2612689
  8. 8.
    Chang, J., Khuller, S., Mukherjee, K.: Active and busy time minimization. In: Proceedings of the 12th MAPSP, pp. 247–249 (2015). http://feb.kuleuven.be/mapsp.2015/Proceedings%20MAPSP%202015.pdf
  9. 9.
    Cohen-Addad, V., Li, Z., Mathieu, C., Milis, I.: Energy-efficient algorithms for non-preemptive speed-scaling. In: Bampis, E., Svensson, O. (eds.) WAOA 2014. LNCS, vol. 8952, pp. 107–118. Springer, Cham (2015). doi:10.1007/978-3-319-18263-6_10 Google Scholar
  10. 10.
    Correa, J.R., Skutella, M., Verschae, J.: The power of preemption on unrelated machines and applications to scheduling orders. Math. Oper. Res. 37(2), 379–398 (2012). http://dx.doi.org/10.1287/moor.1110.0520 MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Flammini, M., Monaco, G., Moscardelli, L., Shachnai, H., Shalom, M., Tamir, T., Zaks, S.: Minimizing total busy time in parallel scheduling with application to optical networks. Theor. Comput. Sci. 411(40–42), 3553–3562 (2010). http://www.sciencedirect.com/science/article/pii/S0304397510002926 MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Ha, S.: Compile-time scheduling of dataflow program graphs with dynamic constructs. Ph.D. thesis, University of California, Berkeley (1992). http://www.eecs.berkeley.edu/Pubs/TechRpts/1992/ERL-92-43.pdf
  13. 13.
    Kalinowski, T., Matsypura, D., Savelsbergh, M.W.: Incremental network design with maximum flows. Eur. J. Oper. Res. 242(1), 51–62 (2015). http://www.sciencedirect.com/science/article/pii/S0377221714008078 MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Khandekar, R., Schieber, B., Shachnai, H., Tamir, T.: Real-time scheduling to minimize machine busy times. J. Sched. 18(6), 561–573 (2015). http://dx.doi.org/10.1007/s10951-014-0411-z MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Mertzios, G.B., Shalom, M., Voloshin, A., Wong, P.W.H., Zaks, S.: Optimizing busy time on parallel machines. In: Proceedings of the 26th IPDPS, pp. 238–248. IEEE (2012). http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6267839
  16. 16.
    Nurre, S.G., Cavdaroglu, B., Mitchell, J.E., Sharkey, T.C., Wallace, W.A.: Restoring infrastructure systems: an integrated network design and scheduling (INDS) problem. Eur. J. Oper. Res. 223(3), 794–806 (2012). http://www.sciencedirect.com/science/article/pii/S0377221712005310 MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Parsons, E.W., Sevcik, K.C.: Multiprocessor scheduling for high-variability service time distributions. In: Feitelson, D.G., Rudolph, L. (eds.) JSSPP 1995. LNCS, vol. 949, pp. 127–145. Springer, Heidelberg (1995). doi:10.1007/3-540-60153-8_26 CrossRefGoogle Scholar
  18. 18.
    Schulz, A.S., Skutella, M.: Scheduling unrelated machines by randomized rounding. SIAM J. Discret. Math. 15(4), 450–469 (2002). http://dx.doi.org/10.1137/S0895480199357078 MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Soper, A.J., Strusevich, V.A.: Power of preemption on uniform parallel machines. In: Proceedings of the 17th APPROX. LIPIcs, vol. 28, pp. 392–402. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2014). http://drops.dagstuhl.de/opus/volltexte/2014/4711

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Fidaa Abed
    • 1
  • Lin Chen
    • 2
  • Yann Disser
    • 3
  • Martin Groß
    • 4
  • Nicole Megow
    • 5
  • Julie Meißner
    • 6
  • Alexander T. Richter
    • 7
  • Roman Rischke
    • 8
  1. 1.University of JeddahJeddahSaudi Arabia
  2. 2.University of HoustonHoustonUSA
  3. 3.TU DarmstadtDarmstadtGermany
  4. 4.University of WaterlooWaterlooCanada
  5. 5.University of BremenBremenGermany
  6. 6.TU BerlinBerlinGermany
  7. 7.TU BraunschweigBraunschweigGermany
  8. 8.TU MünchenMunichGermany

Personalised recommendations