On-Line Algorithms, Real Time, the Virtue of Laziness, and the Power of Clairvoyance

  • Giorgio Ausiello
  • Luca Allulli
  • Vincenzo Bonifaci
  • Luigi Laura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


In several practical circumstances we have to solve a problem whose instance is not a priori completely known. Situations of this kind occur in computer systems and networks management, in financial decision making, in robotics etc. Problems that have to be solved without a complete knowledge of the instance are called on − line problems. The analysis of properties of on-line problems and the design of algorithmic techniques for their solution (on − line algorithms) have been the subject of intense study since the 70-ies, when classical algorithms for scheduling tasks in an on-line fashion [22] and for handling paging in virtual storage systems [11] have been first devised. In the 80-ies formal concepts for analyzing and measuring the quality of on-line algorithms have been introduced [40] and the notion of competitive analysis has been defined as the ratio between the value of the solution that is obtained by an on-line algorithm and the value of the best solution that can be achieved by an optimum off-line algorithm that has full knowledge of the problem instance. Since then a very broad variety of on-line problems have been addressed in the literature [14, 19]: memory allocation and paging, bin packing, load balancing in multiprocessor systems, updating and searching a data structure (e.g. a list), scheduling, financial investment, etc.


Completion Time Travel Salesman Problem Competitive Ratio Online Algorithm Competitive Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Afrati, F., Cosmadakis, S., Papadimitriou, C.H., Papageorgiou, G., Papakostantinou, N.: The complexity of the travelling repairman problem. Informatique Theorique et Applications 20(1), 79–87 (1986)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Albers, S.: On the influence of lookahead in competitive paging algorithms. Algorithmica 18(3), 283–305 (1997)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Albers, S.: A competitive analysis of the list update problem with lookahead. Theor. Comput. Sci. 197(1-2), 95–109 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Allulli, L., Ausiello, G., Laura, L.: On the power of lookahead in on-line vehicle routing problems. Technical Report TR-02-05, Dipartimento di Informatica e Sistemistica, Universitá di Roma La Sapienza (2005)Google Scholar
  5. 5.
    Allulli, L., Ausiello, G., Laura, L.: On the power of lookahead in on-line vehicle routing problems [extended abstract]. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 728–736. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Ausiello, G., Bonifaci, V., Laura, L.: The on-line asymmetric traveling salesman problem. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 306–317. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Ausiello, G., Demange, M., Laura, L., Paschos, V.: Algorithms for the on-line quota traveling salesman problem. Inf. Process. Lett. 92(2), 89–94 (2004)CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L., Talamo, M.: Algorithms for the on-line travelling salesman. Algorithmica 29(4), 560–581 (2001)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Becchetti, L., Leonardi, S.: Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines. Journal of the ACM 51(4), 517–539 (2004)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Becchetti, L., Leonardi, S., Marchetti-Spaccamela, A., Pruhs, K.: Semiclairvoyant scheduling. Theoretical Computer Science 324(2-3), 325–335 (2004)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Belady, L.: A study of replacement algorithms for a virtual-storage computer. IBM Sys. J. 5(2), 78–101 (1966)CrossRefGoogle Scholar
  12. 12.
    Blom, M., Krumke, S.O., de Paepe, W.E., Stougie, L.: The online-TSP against fair adversaries. INFORMS Journal on Computing 13, 138–148 (2001)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Bonifaci, V., Lipmann, M., Stougie, L.: Online multi-server dial-a-ride problems. Technical Report 02-06, Department of Computer and Systems Science, University of Rome La Sapienza, Rome, Italy (2006)Google Scholar
  14. 14.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  15. 15.
    Chen, B., Vestjens, A.P.A.: Scheduling on identical machines: How good is LPT in an on-line setting? Operations Research Letters 21, 165–169 (1998)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Correa, J.R., Wagner, M.R.: LP-based online scheduling: From single to parallel machines. In: Jünger, M., Kaibel, V. (eds.) IPCO 2005. LNCS, vol. 3509, pp. 196–209. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    de Paepe, W.: Complexity Results and Competitive Analysis for Vehicle Routing Problems. PhD thesis, Technical University of Eindhoven (2002)Google Scholar
  18. 18.
    Feuerstein, E., Stougie, L.: On-line single-server dial-a-ride problems. Theoretical Computer Science 268, 91–105 (2001)CrossRefMathSciNetzbMATHGoogle Scholar
  19. 19.
    Fiat, A., Woeginger, G.J. (eds.): Online Algorithms: The State of the Art. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  20. 20.
    Garg, N.: A 3-approximation for the minimum tree spanning k vertices. In: Proc. 37th Symp. Foundations of Computer Science (FOCS), pp. 302–309 (1996)Google Scholar
  21. 21.
    Goemans, M., Kleinberg, J.: An improved approximation ratio for the minimum latency problem. Mathematical Programming 82(1), 111–124 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  22. 22.
    Graham, R.L.: Bounds for certain multiprocessing anomalies. Bell System Technical Journal 45, 1563–1581 (1966)Google Scholar
  23. 23.
    Grove, E.F.: Online bin packing with lookahead. In: SODA 1995: Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, pp. 430–436 (1995)Google Scholar
  24. 24.
    Hauptmeier, D., Krumke, S.O., Rambau, J.: The online dial-a-ride problem under reasonable load. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds.) CIAC 2000. LNCS, vol. 1767, pp. 125–136. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  25. 25.
    Irani, S.: Coloring inductive graphs on-line. Algorithmica 11(1), 53–72 (1994)CrossRefMathSciNetzbMATHGoogle Scholar
  26. 26.
    Jaillet, P., Wagner, M.: Online routing problems: Value of advanced information and improved competitive ratios. Under review, Transportation Science (2005), Available at
  27. 27.
    Jünger, M., Reinelt, G., Rinaldi, G.: The traveling salesman problem. In: Ball, M.O., Magnanti, T., Monma, C.L., Nemhauser, G. (eds.) Network Models, Handbook on Operations Research and Management Science, vol. 7, pp. 225–230. Elsevier, North Holland (1995)Google Scholar
  28. 28.
    Kao, M.-Y., Tate, S.R.: Online matching with blocked input. Inf. Process. Lett. 38(3), 113–116 (1991)CrossRefMathSciNetzbMATHGoogle Scholar
  29. 29.
    Koutsoupias, E., Papadimitriou, C.: On the k-server conjecture. Journal of the ACM 42, 971–983 (1995)CrossRefMathSciNetzbMATHGoogle Scholar
  30. 30.
    Krumke, S.O.: Online optimization: Competitive analysis and beyond. Habilitation Thesis, Technical University of Berlin (2001)Google Scholar
  31. 31.
    Krumke, S.O., de Paepe, W.E., Poensgen, D., Stougie, L.: News from the online traveling repairman. In: Proc. 28th International Colloquium on Automata, Languages, and Programming (ICALP), pp. 487–499 (2001)Google Scholar
  32. 32.
    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.) APPROX 2002. LNCS, vol. 2462, pp. 200–214. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  33. 33.
    Laura, L.: Risoluzione on-line di problemi dial-a-ride Master’s thesis. University of Rome, La Sapienza (1999)Google Scholar
  34. 34.
    Lipmann, M.: On-Line Routing. PhD thesis, Technical University of Eindhoven (2003)Google Scholar
  35. 35.
    Lipmann, M., Lu, X., de Paepe, W., Sitters, R., Stougie, L.: On-line dial-a-ride problems under a restricted information model. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 674–685. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  36. 36.
    Motwani, R., Phillips, S., Torng, E.: Non-clairvoyant scheduling. Theoretical Computer Science 130(1), 17–47 (1994)CrossRefMathSciNetzbMATHGoogle Scholar
  37. 37.
    Pruhs, K., Sgall, J., Torng, E.: Online scheduling. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms: The State of the Art, pp. 159–176. Springer, Heidelberg (1998)Google Scholar
  38. 38.
    Sgall, J.: On-line scheduling. In: Fiat, A., Woeginger, G.J. (eds.) Online Algorithms: The State of the Art, pp. 196–231. Springer, Heidelberg (1998)Google Scholar
  39. 39.
    Sitters, R., Stougie, L.: The minimum latency problem is np-hard for weighted trees. In: Proc. 9th Integer Programming and Combinatorial Optimization Conference, pp. 230–239 (2002)Google Scholar
  40. 40.
    Sleator, D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28(2), 202–208 (1985)CrossRefMathSciNetGoogle Scholar
  41. 41.
    Subramani, K.: Totally clairvoyant scheduling with relative timing constraints. In: Seventh International Conference on Verification, Model (2006)Google Scholar
  42. 42.
    Vestjens, A.P.A.: On-line Machine Scheduling. PhD thesis, Eindhoven University of Technology, The Netherlands (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Giorgio Ausiello
    • 1
  • Luca Allulli
    • 1
  • Vincenzo Bonifaci
    • 1
    • 2
  • Luigi Laura
    • 1
  1. 1.Department of Computer and Systems ScienceUniversity of Rome, “La Sapienza”RomaItaly
  2. 2.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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