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A new approach for bicriteria partitioning problem

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Abstract

In this paper, we propose a new method to evaluate the performance of an algorithm for bicriteria optimization problems, specifically worst-case boundary, which is more accurate than the original ones. We use a typical multicriteria partitioning problem to serve as an example to illustrate the strength and features of our method. We show the worst-case boundary of the classical \(LS\) algorithm, and make comparison on the efficiency between the new method and the former ones. The limitation of simultaneous optimization is also shown in our paper.

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References

  1. Alon, N., Azar, Y., Woeginger, G.J., Yadid, T.: Approximation schemes for scheduling on parallel machines. J. Sched. 1(1), 55–66 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Angel, E., Bampis, E., Fishkin, A.V.: A note on scheduling to meet two min-sum objectives. Oper. Res. Lett. 35, 69–73 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  3. Aslam, J., Rasala, A., Stein, C., Young, N.: Improved bicriteria existence theorems for scheduling. In: Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 846–847 (1999)

  4. Babel, L., Kellerer, H., Kotov, V.: The \(k\)-partitioning problem. Math. Methods Oper. Res. 47, 59–82 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bampis, E., Kononov, A.: Bicriteria approximation algorithms for scheduling problems with communications delays. J. Sched. 8, 281–294 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bansal, N., Sviridenko, M.: The Santa Claus problem. In: Proceedings of the 38th ACM Symposium on Theory of Computing, pp. 31–40 (2006)

  7. Csirik, J., Kellerer, H., Woeginger, G.: The exact LPT-bound for maximizing the minimum completion time. Oper. Res. Lett. 11, 281–287 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  8. Dell’Amico, M., Martello, S.: Optimal scheduling of tasks on identical parallel processors. ORSA J. Comput. 7, 191–200 (1995)

    Article  MATH  Google Scholar 

  9. Efraimidis, P.S., Spirakis, P.G.: Approximation schemes for scheduling and covering on unrelated machines. Theor. Comput. Sci. 359, 400–417 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1978)

  11. Graham, R.L.: Bounds for certain multiprocessor anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1966)

    Article  Google Scholar 

  12. Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17, 416–429 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  13. Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discret. Math. 5, 287–326 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  14. Haouari, M., Jemmali, M.: Maximizing the minimum completion time on parallel machines. 4OR Q. J. Oper. Res. 6, 375–392 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kellerer, H., Kotov, V.: A \(3/2\)-approximation algorithm for \(k_i\)-partitioning. Oper. Res. Lett. 39, 359–362 (2011)

    MATH  MathSciNet  Google Scholar 

  16. Rasala, A., Stein, C., Torng, E., Uthaisombut, P.: Existence theorems, lower bounds and algorithms for scheduling to meet two objectives. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 723–731 (2002)

  17. Sahni, S.: Algorithms for scheduling independent tasks. J. Assoc. Comput. Mach. 23, 116–127 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  18. Stein, C., Wein, J.: On the existence of schedules that are near-optimal for both makespan and total weighted completion time. Oper. Res. Lett. 21, 115–122 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. T’kindt, V., Billaut, J.C.: Multicriteria Scheduling: Theory, Models and Algorithms, 2nd edn. Springer, Berlin (2006)

    Google Scholar 

  20. Torng, E., Uthaisombut, P.: Lower bounds for srpt-subsequence algorithms for nonpreemptive scheduling. In: Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 973–974 (1999)

  21. Woeginger, G.: A polynomial-time approximation scheme for maximizing the minimum machine completion time. Oper. Res. Lett. 20, 149–154 (1997)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The authors would like to thank the anonymous referees for their careful reading of this article and helpful suggestions. Special thanks a referee for bringing some important literature on bicriteria scheduling to our attention. Supported by the National Natural Science Foundation of China (10971191, 11271324), Zhejiang Provincial Natural Science Foundation of China (LR12A01001) and Fundamental Research Funds for the Central Universities

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Mengyang Gu & Yujie Yan

  2. Department of Mathematics, State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Zhiyi Tan

  3. School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Binzhou Xia

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  1. Mengyang Gu
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  2. Zhiyi Tan
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  3. Binzhou Xia
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  4. Yujie Yan
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Correspondence to Zhiyi Tan.

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Gu, M., Tan, Z., Xia, B. et al. A new approach for bicriteria partitioning problem. Optim Lett 9, 1025–1037 (2015). https://doi.org/10.1007/s11590-014-0796-9

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  • DOI: https://doi.org/10.1007/s11590-014-0796-9

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