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 


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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)MathSciNetMATHGoogle Scholar
  2. 2.
    Albers, S.: On the influence of lookahead in competitive paging algorithms. Algorithmica 18(3), 283–305 (1997)CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Albers, S.: A competitive analysis of the list update problem with lookahead. Theor. Comput. Sci. 197(1-2), 95–109 (1998)CrossRefMathSciNetMATHGoogle 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)CrossRefMathSciNetMATHGoogle 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)CrossRefMathSciNetMATHGoogle 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)CrossRefMathSciNetMATHGoogle Scholar
  10. 10.
    Becchetti, L., Leonardi, S., Marchetti-Spaccamela, A., Pruhs, K.: Semiclairvoyant scheduling. Theoretical Computer Science 324(2-3), 325–335 (2004)CrossRefMathSciNetMATHGoogle 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)MATHGoogle 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)CrossRefMathSciNetMATHGoogle Scholar
  19. 19.
    Fiat, A., Woeginger, G.J. (eds.): Online Algorithms: The State of the Art. Springer, Heidelberg (1998)MATHGoogle 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)CrossRefMathSciNetMATHGoogle 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)CrossRefMathSciNetMATHGoogle 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 http://web.mit.edu/jaillet/www/general/publications.html
  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)CrossRefMathSciNetMATHGoogle Scholar
  29. 29.
    Koutsoupias, E., Papadimitriou, C.: On the k-server conjecture. Journal of the ACM 42, 971–983 (1995)CrossRefMathSciNetMATHGoogle 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)CrossRefMathSciNetMATHGoogle 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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