Abstract
In this paper we describe a general grouping technique to devise faster and simpler approximation schemes for several scheduling problems. We illustrate the technique on two different scheduling problems: scheduling on unrelated parallel machines with costs and the job shop scheduling problem. The time complexity of the resulting approximation schemes is always linear in the number n of jobs, and the multiplicative constant hidden in the O(n) running time is reasonably small and independent of the error ε.
Supported by Swiss National Science Foundation project 21-55778.98, “Resource Allocation and Scheduling in Flexible Manufacturing Systems”, by the “Metaheuristics Network”, grant HPRN-CT-1999-00106, and by the “Thematic Network APPOL”, Approximation and on-line algorithms, grant IST-1999-14084.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A.K. Amoura, E. Bampis, C. Kenyon, and Y. Manoussakis, Scheduling independent multiprocessor tasks, Proceedings of the 5th Annual European Symposium on Algorithms, vol. 1284, LNCS, 1997, pp. 1–12.
J. Chen and A. Miranda, A polynomial time approximation scheme for general multiprocessor job scheduling, Proceedings of the 31st Annual ACM Symposium on the Theory of Computing, 1999, pp. 418–427.
M. R. Garey and D. S. Johnson, Computers and intractability; a guide to the theory of np-completeness, W.H. Freeman, 1979.
M. D. Grigoriadis and L. G. Khachiyan, Coordination complexity of parallel price-directive decomposition, Mathematics of Operations Research 21 (1996), 321–340.
L.A. Goldberg, M. Paterson, A. Srinivasan, and E. Sweedyk, Better approximation guarantees for job-shop scheduling, SIAM Journal on Discrete Mathematics 14 (2001), no. 1, 67–92.
E. Horowitz and S. Sahni, Exact and approximate algorithms for scheduling non-identical processors, Journal of the ACM 23 (1976), 317–327.
K. Jansen and L. Porkolab, Improved approximation schemes for scheduling unrelated parallel machines, Proceedings of the 31st Annual ACM Symposium on the Theory of Computing, 1999, pp. 408–417.
K. Jansen and L. Porkolab, Linear-time approximation schemes for scheduling malleable parallel tasks, Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, 1999, pp. 490–498.
K. Jansen and L. Porkolab, Polynomial time approximation schemes for general multiprocessor job shop scheduling, ICALP’00, 2000, pp. 878–889.
K. Jansen, R. Solis-Oba, and M. Sviridenko, Makespan minimization in job shops: a polynomial time approximation scheme, Proceedings of the 31st Annual ACM Symposium on the Theory of Computing, 1999, pp. 394–399.
K. Jansen, R. Solis-Oba, and M. Sviridenko, A linear time approximation scheme for the job shop scheduling problem, APPROX’99, vol. 1671, 1999, pp. 177–188.
E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys, Sequencing and scheduling: Algorithms and complexity, Handbook in Operations Research and Management Science 4 (1993), 445–522.
J. K. Lenstra, D. B. Shmoys, and E. Tardos, Approximation algorithms for scheduling unrelated parallel machines, Mathematical Programming 46 (1990), 259–271.
S. V. Sevastianov, On some geometric methods in scheduling theory: a survey, Discrete Applied Mathematics 55 (1994), 59–82.
D.B. Shmoys and E. Tardos, An approximation algorithm for the generalized assignment problem, Mathematical Programming (1993), 461–474.
D.B. Shmoys, C. Stein and J. Wein, Improved approximation algorithms for shop scheduling problems, SIAM Journal on Computing 23 (1994), 617–632.
D.P. Williamson, L.A. Hall, J.A. Hoogeveen, C.A.J. Hurkens, J.K. Lenstra, S.V. Sevastianov, and D.B. Shmoys, Short shop schedules, Operations Research 45 (1997), 288–294.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fishkin, A.V., Jansen, K., Mastrolilli, M. (2001). Grouping Techniques for Scheduling Problems: Simpler and Faster. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_17
Download citation
DOI: https://doi.org/10.1007/3-540-44676-1_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42493-2
Online ISBN: 978-3-540-44676-7
eBook Packages: Springer Book Archive