Makespan minimization in job shops: A linear time approximation scheme

SIAM Journal on Discrete Mathematics

Volumn 16, Issue 2, 2003, Pages 288-300

  Jansen, Klaus ^a   Solis Oba, Roberto ^b   Sviridenko, Maxim ^c  

^a UNIVERSITY OF KIEL   (Germany)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

^c IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Approximation algorithm; Approximation scheme; Job shop; Scheduling

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; JOB ANALYSIS; MATRIX ALGEBRA; POLYNOMIAL APPROXIMATION; SCHEDULING; VECTORS;

APPROXIMATION ALGORITHM; JOB SHOP SCHEDULING; MAKESPAN MINIMIZATION; POLYNOMIAL TIME APPROXIMATION SCHEME;

LINEAR PROGRAMMING;

EID: 0038137159     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480199363908     Document Type: Article

References (16)

1. L. A. Goldberg, M. Paterson, A Srinivasan, and E. Sweedyk, Better approximation guarantees for job-shop scheduling, SIAM J. Discrete Math., 14 (2000), pp. 67-92.
2. M. D. Grigoriadis and L. G. Khachiyan, Coordination complexity of parallel price-directive decomposition, Math. Oper. Res., 21 (1996), pp. 321-340.
3. L. A. Hall, Approximability of flow shop scheduling, Math. Programming, 82 (1998), pp. 175-190.
4. K. Jansen, R. Solis-Oba, and M. I. Sviridenko, Makespan minimnization in job shops: A polynomial time approximation scheme, in Proceedings of the 31st Annual ACM Symposium on Theory of Computing, Atlanta, GA, 1999, pp. 394-399
5. K. Jansen, R. Solis-Oba, and M. I. Sviridenko, A linear time approximation scheme for the job shop scheduling problem, in Proceedings of the Second Workshop on Approximation Algorithms, Berkeley, CA, 1999, Lecture Notes in Comput. Sci. 1671, Springer, Berlin, 1999, pp. 177-188.
6. E. L. Lawler, J. K. Lenstra, A. H. G. Rinooy Kan, and D. B. Shmoys, Sequencing and scheduling: Algorithms and complexity, in Handbooks in Operations Research and Management Science, Vol. 4, Logistics of Production and Inventory, S. C. Graves, A. H. G. Rinooy Kan, and P. H. Zipkin, eds., North-Holland, Amsterdam, 1993, pp. 445-522.
7. T. Leighton, B. Maggs, and S. Rao, Packet routing and job-shop scheduling in O(congestion + dilation) steps, Combinatorica, 14 (1994), pp. 167-186.
8. T. Leighton, B. Maggs, and A. Richa, Fast algorithms for finding O(congestion + dilation) packet routing schedules, Combinatorica, 19 (1999), pp. 375-401
9. C. N. Potts, Analysis of a linear programming heuristic for scheduling unrelated parallel machines, Discrete Appl. Math., 10 (1985), pp. 155-164.
10. S. V. Sevastianov, Bounding algorithm for the routing problem with arbitrary paths and alternative servers, Cybernetics, 22 (1986), pp. 773-780.
11. S. V. Sevastianov, On some geometric methods in scheduling theory: A survey, Discrete Appl. Math., 55 (1994), pp. 59-82.
12. S. V. Sevastianov and G. J. Woeginger, Makespan minimization in preemptive two machine job shops, Computing, 60 (1998), pp. 73-79.
13. S. V. Sevastianov and G. J. Woeginger, Makespan minimization in open shops: A polynomial time approximation scheme, Math. Programming, 82 (1998), pp. 191-198.
14. D. B. Shmoys, unpublished manuscript.
15. D. B. Shmoys, C. Stein, and J. Wein, Improved approximation algorithms for shop scheduling problems, SIAM J. Comput., 23 (1994), pp. 617-632.
16. 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, Oper. Res., 45 (1997), pp. 288-294.