Abstract
Consider n independent jobs and m uniform machines in parallel. Each job has a processing requirement and a deadline. All jobs are available for processing at time t = 0. Job j must complete its processing before or at its deadline and preemptions are allowed. A set of jobs is said to be feasible if there exists a schedule that meets all the deadlines. We present a polynomial-time algorithm that given a feasible set of jobs, constructs a schedule that minimizes the total completion time ΣCj. In the classical α | β | γ scheduling notation, this problem is referred to as Qm | prmt, d¯j | ΣCj. It is well known that a generalization of this problem with regard to its machine environment results in an NP-hard problem.
- Baker, K. R. 1974. Introduction to Sequencing and Scheduling, Wiley, New York.]]Google Scholar
- Cho, Y., and Sahni, S. 1980. Scheduling independent tasks with due times on a uniform processor system. J. ACM. 20, 550--563.]] Google ScholarDigital Library
- Du, J., and Leung, J. Y.-T. 1993. Minimizing mean flow time with release time and deadline constraints. J. Algor. 14, 45--68.]] Google ScholarDigital Library
- Du, J., Leung, J. Y.-T., and Young, G. H. 1990. Minimizing mean flow time with release time constraint. Theoret. Comput. Sci. 75, 347--355.]] Google ScholarDigital Library
- Federgruen, A., and Groenevelt, H. 1986. Preemptive scheduling of uniform machines by ordinary network flow techniques. Manage. Sci. 32, 341--349.]]Google ScholarDigital Library
- Gonzalez, T. F. 1978. Minimizing the mean and maximum finishing time on uniform processors. Tech. Rep. CS-78-22. Dept. Comput. Sci. The Pennsylvania State University, University Park, PA.]]Google Scholar
- Gonzalez, T. F., and Sahni, S. 1978. Preemptive scheduling of uniform processor systems. J. ACM. 25, 92--101.]] Google ScholarDigital Library
- Graham, R. L., Lawler, E. L., Lenstra, J. K., and Rinnooy Kan, A. H. G. 1979. Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 5, 287--326.]]Google ScholarCross Ref
- Horvath, E. C., Lam, S., and Sethi, R. 1976. A level algorithm for preemptive scheduling. J. ACM. 23, 317--327.]]Google Scholar
- Lawler, E. L. 1982. Recent results in the theory of machine scheduling. In Mathematical Programming: The State of the Art. A. Bachem, M. Grotschel, and B. Korte, Eds. Springer-Verlag, Berlin, Germany.]]Google Scholar
- Lenstra, J. K. 1977. Sequencing by Enumerative Methods. Mathematical Centre Tracts 69, Mathematisch Centrum, Amsterdam, the Netherlands.]]Google Scholar
- Leung, J. Y.-T., and Pinedo, M. 2003. Minimizing total completion time with parallel machines with deadline constraints. SIAM J. Comput. 32, 5, 1370--1388.]] Google ScholarDigital Library
- Liu, J. W. S., and Yang, A. 1974. Optimal scheduling of independent tasks on heterogeneous computing systems. In Proceedings of the ACM Annual Conference (San Diego, CA, Nov.). ACM, New York, pp. 38--45.]] Google ScholarDigital Library
- McCormick, S. T., and Pinedo, M. 1995. Scheduling n independent on m uniform machines with both flow time and makespan objectives: A parametric analysis. ORSA J. Comput. 7, 63--77.]]Google ScholarCross Ref
- Pinedo, M. 2002. Scheduling: Theory, Algorithms and Systems. Prentice-Hall, Englewood Cliffs, NJ.]]Google Scholar
- Sitters, R. A. 2001. Two NP-hardness results for preemptive minsum scheduling of unrelated parallel machines. In Proceedings of the 8th International IPCO Conference, Lecture Notes in Computer Science, vol. 2081. Springer-Verlag, New York, pp. 396--405.]] Google ScholarDigital Library
- Smith, W. E. 1956. Various optimizers for single-stage production. Nav. Res. Log. Quart. 3, 59--66.]]Google ScholarCross Ref
Index Terms
- Minimizing total completion time on uniform machines with deadline constraints
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