2-Approximation Algorithm for Parallel Machine Scheduling with Consecutive Eligibility

주어진 구간내의 기계에서만 생산 가능한 병렬기계문제에 대한 2-근사 알고리듬

  • Hwang, Hark-Chin (Department of lndustrial Engineering Chosun University) ;
  • Kim, Gyutai (Department of lndustrial Engineering Chosun University)
  • 황학진 (조선대학교 산업공학과) ;
  • 김규태 (조선대학교 산업공학과)
  • Published : 2003.09.30

Abstract

We consider the problem of scheduling n jobs on m machines with the objective of minimizing makespan. Each job cannot be eligible to all the machines but to its consecutively eligible set of machines. For this problem, a 2-approximation algorithm, MFFH, is developed. In addition, an example is presented to show the tightness of the algorithm.

Keywords

References

  1. Azar Y., Naor J., Rom R. (1995), The competitiveness of On-Line Assignments, J. Algorithms, 18, 221-237 https://doi.org/10.1006/jagm.1995.1008
  2. Centeno G., Armacost R.L. (1997), Parallel machine scheduling with release time and machine eligibility restrictions, Computers and Industrial Engineering, 33, 273-276 https://doi.org/10.1016/S0360-8352(97)00091-0
  3. Coffman Jr E.G., Garey M.R., Johnson D.S. (1978), An application of bin-packing to multiprocessor scheduling, SIAM J. Comput., 7, 1-17
  4. Friesen D.X. (1984), Tighter bounds for the multi processor scheduling algorithm. SIAM J. Comput., 13, 35-59
  5. Garey M.R., Johnson D.S. (1979), Computers and intractability: A Guide to the theory of NP-Completeness, Freeman, San Francisco
  6. Graham R.L. (1969), Bounds on multiprocessor timing anomalies, SIAM J. Appl. Math., 17, 263-269
  7. Graham, R.L., Lawler E.L., Lenstra J.K. and Rinnooy Kan A.H.G. (1979), Optimization and Approximation in Deterministic Machine Scheduling: A Survey. Annals of Discrete Mathematics, 5, 287-326 https://doi.org/10.1016/S0167-5060(08)70356-X
  8. He Y., Kellerer H., Kotov V. (2000), Linear Compound Algorithms for the Partitioning Problem, Naval Research Logistics, 47, 593-601
  9. Hochbaum D.S., Shmoys D. (1987), Using dual approximation algorithms for scheduling problems: Theoretical and practical results, J. ACM, 34, 144-162 https://doi.org/10.1145/7531.7535
  10. Hochbaum D.S. (1997), Approximation Algorithms for NP-Hard Problems, PWS PUBLISHING COMPANY, Boston, 370-371
  11. Hwang H.-C. (2002), A strongly polynomial algorithm for parallel machine scheduling problem with consecutive eligibility, The Research Institute of industrial Technology Chosun University, 24, 27-31
  12. Ibarra O.H., Kim C.E. (1975), Fast approximation algorithms for the knapsack and sum of subset problems, J. ACM, 22, 463-468 https://doi.org/10.1145/321906.321909
  13. Kellerer H., Pferschy U. (1999), A New Fully Polynomial Approximation Scheme for the Knapsack Problem, Journal of Combinatorial Optimization. 3, 59-71
  14. Lenstra J.K., Shmoys D.B., Tardos E. (1990), Approximation Algorithms for Scheduling Unrelated Parallel Machines, Mathematical Programming. 46, 259-271
  15. Yue M. (1990), On the exact upper bound for the MULTIFIT processor scheduling algorithm, in Operations Research in China, M. Yue (ed.), Vol. 24 of Annals of Operations Research, Baltzer, Basel, Switzerland, 233-259
  16. Vairaktarakis G.L., X. Cai (2001), The Value of Processing Flexibility in Multipurpose Machines, Technical Memorandum Number 744, Weatherhead School of Management. Case Western Reserve University