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Online k-Server Routing Problems

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Abstract

In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the sum of completion times (k-Traveling Repairman Problem). We give competitive algorithms, resource augmentation results and lower bounds for k-server routing problems in a wide class of metric spaces. In some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely, we give a 1+O((log k)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line. We also prove that a similar result cannot hold for the Euclidean plane.

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References

  1. Ascheuer, N., Krumke, S.O., Rambau, J.: Online dial-a-ride problems: Minimizing the completion time. In: Reichel, H., Tison, S. (eds.) Proc. 17th Symp. on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science, vol. 1770, pp. 639–650. Springer, Berlin (2000)

    Google Scholar 

  2. Ausiello, G., Bonifaci, V., Laura, L.: The on-line asymmetric traveling salesman problem. J. Discrete Algorithms (2007). doi:10.1016/j.jda.2007.03.002

    Google Scholar 

  3. Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L., Talamo, M.: Algorithms for the on-line travelling salesman. Algorithmica 29(4), 560–581 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Blom, M., Krumke, S.O., de Paepe, W.E., Stougie, L.: The online TSP against fair adversaries. INFORMS J. Comput. 13(2), 138–148 (2001)

    Article  MathSciNet  Google Scholar 

  5. Bonifaci, V.: Models and algorithms for online server routing. PhD thesis, Technical University Eindhoven, The Netherlands (2007). Available at http://www.dis.uniroma1.it/~bonifaci/papers/phdthesis-tue.pdf

  6. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  7. Borodin, A., El-Yaniv, R.: On randomization in online computation. Inf. Comput. 150, 244–267 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Chaudhuri, K., Godfrey, B., Rao, S., Talwar, K.: Paths, trees, and minimum latency tours. In: Proc. 44th Symp. on Foundations of Computer Science, pp. 36–45 (2003)

  9. Chen, B., Vestjens, A.P.A.: Scheduling on identical machines: How good is LPT in an on-line setting? Oper. Res. Lett. 21(4), 165–169 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Correa, J.R., Wagner, M.R.: LP-based online scheduling: From single to parallel machines. In: Integer Programming and Combinatorial Optimization. Lecture Notes in Computer Science, vol. 3509, pp. 196–209. Springer, Berlin (2005)

    Google Scholar 

  11. Fakcharoenphol, J., Harrelson, C., Rao, S.: The k-traveling repairman problem. In: Proc. 14th Symp. on Discrete Algorithms, pp. 655–664 (2003)

  12. Feuerstein, E., Stougie, L.: On-line single-server dial-a-ride problems. Theor. Comput. Sci. 268(1), 91–105 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Frederickson, G.N., Hecht, M.S., Kim, C.E.: Approximation algorithms for some routing problems. SIAM J. Comput. 7(2), 178–193 (1978)

    Article  MathSciNet  Google Scholar 

  14. Hauptmeier, D., Krumke, S.O., Rambau, J.: The online dial-a-ride problem under reasonable load. In: Bongiovanni, G., Gambosi, G., Petreschi, R. (eds.) Proc. 4th Italian Conference on Algorithms and Complexity. Lecture Notes in Computer Science, vol. 1767, pp. 125–136. Springer, Berlin (2000)

    Google Scholar 

  15. Jothi, R., Raghavachari, B.: Minimum latency tours and the k-traveling repairmen problem. In: Farach-Colton, M. (ed.) Proc. 6th Symp. Latin American Theoretical Informatics. Lecture Notes in Computer Science, vol. 2976, pp. 423–433. Springer, Berlin (2004)

    Google Scholar 

  16. Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. Assoc. Comput. Mach. 47(4), 214–221 (2000)

    MathSciNet  Google Scholar 

  17. Krumke, S.O.: Personal communication (2006)

  18. Krumke, S.O., de Paepe, W.E., Poensgen, D., Stougie, L.: News from the online traveling repairman. Theor. Comput. Sci. 295(1–3), 279–294 (2003)

    Article  MATH  Google Scholar 

  19. Krumke, S.O., Laura, L., Lipmann, M., Marchetti-Spaccamela, A., de Paepe, W.E., Poensgen, D., Stougie, L.: Non-abusiveness helps: an O(1)-competitive algorithm for minimizing the maximum flow time in the online traveling salesman problem. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) Proc. 5th Int. Workshop on Approximation Algorithms for Combinatorial Optimization. Lecture Notes in Computer Science, vol. 2462, pp. 200–214. Springer, Berlin (2002)

    Chapter  Google Scholar 

  20. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A., Shmoys, D.B. (eds.): The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. Wiley, Chichester (1985)

    MATH  Google Scholar 

  21. Lipmann, M.: On-line routing. PhD thesis, Technical University Eindhoven, The Netherlands (2003)

  22. Lipmann, M., Lu, X., de Paepe, W.E., Sitters, R.A., Stougie, L.: On-line dial-a-ride problems under a restricted information model. Algorithmica 40(4), 319–329 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  23. Manasse, M., McGeoch, L.A., Sleator, D.: Competitive algorithms for server problems. J. Algorithms 11(2), 208–230 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  24. Sgall, J.: On-line scheduling. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms: the State of the Art, pp. 196–231. Springer, Berlin (1998)

    Chapter  Google Scholar 

  25. Stougie, L., Vestjens, A.P.A.: Randomized on-line scheduling: How low can’t you go? Oper. Res. Lett. 30(2), 89–96 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dept. Computer and Systems Science, University of Rome “La Sapienza”, Rome, Italy

    Vincenzo Bonifaci

  2. Dept. Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands

    Vincenzo Bonifaci & Leen Stougie

  3. Center for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands

    Leen Stougie

Authors
  1. Vincenzo Bonifaci
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  2. Leen Stougie
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Correspondence to Vincenzo Bonifaci.

Additional information

An extended abstract of this work has appeared in the proceedings of the 4th Workshop on Approximation and Online Algorithms, September 2006.

Research of V. Bonifaci partly supported by the Dutch Ministry of Education, Culture and Science through a Huygens scholarship.

Research of L. Stougie partly supported by MRT Network ADONET of the European Community (MRTN-CT-2003-504438) and the Dutch BSIK/BRICKS project.

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Bonifaci, V., Stougie, L. Online k-Server Routing Problems. Theory Comput Syst 45, 470–485 (2009). https://doi.org/10.1007/s00224-008-9103-4

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  • DOI: https://doi.org/10.1007/s00224-008-9103-4

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