Abstract
The problem of scheduling jobs with release dates on a single machine so as to minimize total completion time has long been know to be strongly NP-complete. Recently, a polynomial-time approximation scheme (PTAS) was found for this problem. We implemented this algorithm to compare its performance with several other known algorithms for this problem. We also developed several good algorithms based on this PTAS that run faster by sacrificing the performance guarantee. Our results indicate that the ideas used by this PTAS lead to improved algorithms.
Research partially supported by NSF Career Award CCR-9624828, NSF Grant EIA-98-02068, NSF Grant DMI-9970063 and an Alfred P. Sloane Foundation Fellowship.
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F. Afrati, E. Bampis, C. Chekuri, D. Karger, C. Kenyon, S. Khanna, I. Milis, M. Queyranne, M. Skutella, C. Stein, and M. Sviridenko. Approximation schemes for minimizing average weighted completion time with release dates. 40th Annual Symposium on Foundations of Computer Science, pages 32–43, 1999.
Ramesh Chandra. On n/1/F dynamic deterministic systems. Naval Research Logistics Quarterly, 26:537–544, 1979.
Chekuri C., Motwani R., Natarajan B., and Stein C. Approximation techniques for average completion time scheduling. Proceedings of Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 609–18, 1997.
Chengbin Chu. One-machine scheduling for minimizing total flow time with release dates. In Proceedings of Rensselaer’s Second Conference on C.I.M, pages 570–576, 1990.
Chengbin Chu. A branch-and-bound algorithm to minimize total flow time with unequal release dates. Naval Research Logistics, 39:859–875, 1992.
Pedro G. Gazmuri. Probabilistic analysis of a machine scheduling problem. Mathematics of Operations Research, 10(2):328–339, 1985.
Michel X. Goemans. Improved approximation algorithms for scheduling with release dates. In Proceedings of Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, 1997.
A.M.A Hariri and C.N. Potts. An algorithm for single machine sequencing with release dates to minimize total weighted completion time. Discrete Applied Mathematics, 5:99–109, 1983.
J.A. Hoogeveen and A.P.A Vestjens. Optimal on-line algorithms for single-machine scheduling. In Proceedings of the Fifth Conference On Integer Programming and Combinatorial Optimization, pages 404–414, 1996.
O.H. Ibarra and C.E. Kim. Fast approximation algorithms for the knapsack and sum of subset problems. Journal of the Association for Computing Machinery, 22:463–468, 1975.
Hans Kellerer, Thomas Tautenhahn, and Gerhard J. Woeginger. Approximability and nonapproximability results for minimizing total flow time on a single machine. SI AM Journal of Computing, 28(4):1155–1166, 1999.
J.K. Lenstra, A.H.G. Rinnooy Kan, and P. Brucker. Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1:343–362, 1977.
C. Phillips, C. Stein, and J. Wein. Minimizing average completion time in the presence of release dates. Mathematical Programming, 82:199–223, 1998.
Andreas S. Schulz and Martin Skutella. Scheduling-LPs bear probabilities: Randomized approximations for min-sum criteria. Technical Report 533/1996, Technische Universität Berlin, Fachbereich Mathematik, 1996.
W.E. Smith. Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3:59–66, 1956.
E. Torng and P. Uthaisombut. Lower bounds for srpt-subsequence algorithms for nonpreemptive scheduling. In Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pages 973–974, 1999.
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Hepner, C., Stein, C. (2001). Implementation of a PTAS for Scheduling with Release Dates. In: Buchsbaum, A.L., Snoeyink, J. (eds) Algorithm Engineering and Experimentation. ALENEX 2001. Lecture Notes in Computer Science, vol 2153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44808-X_17
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DOI: https://doi.org/10.1007/3-540-44808-X_17
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