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Volumn 149, Issue 2, 2003, Pages 355-376

Identical parallel machines vs. unit-time shops and preemptions vs. chains in scheduling complexity

Author keywords

Complexity; Parallel machines; Reduction; Scheduling; Shop; Unit processing time

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; JOB ANALYSIS; POLYNOMIALS; PROBLEM SOLVING; SCHEDULING; TREES (MATHEMATICS);

EID: 0037846121     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(02)00767-1     Document Type: Conference Paper
Times cited : (28)

References (83)
  • 1
    • 0021301027 scopus 로고
    • Openshop and flowshop scheduling problems to minimize sum of completion times
    • Adiri I., Amit N. Openshop and flowshop scheduling problems to minimize sum of completion times. Computers & Operations Research. 11:1984;275-284.
    • (1984) Computers & Operations Research , vol.11 , pp. 275-284
    • Adiri, I.1    Amit, N.2
  • 2
    • 0037851109 scopus 로고    scopus 로고
    • Scheduling equal-length jobs on identical parallel machines
    • Baptiste P. Scheduling equal-length jobs on identical parallel machines. Discrete Applied Mathematics. 103:2000;21-32.
    • (2000) Discrete Applied Mathematics , vol.103 , pp. 21-32
    • Baptiste, P.1
  • 3
    • 0037846127 scopus 로고    scopus 로고
    • On minimizing the weighted number of late jobs in unit execution time open-shops
    • this issue
    • P. Baptiste, On minimizing the weighted number of late jobs in unit execution time open-shops, European Journal of Operational Research, this issue.
    • European Journal of Operational Research
    • Baptiste, P.1
  • 4
    • 0035362830 scopus 로고    scopus 로고
    • On preemption redundancy in scheduling unit processing time jobs on two parallel machines
    • Baptiste P., Timkovsky V.G. On preemption redundancy in scheduling unit processing time jobs on two parallel machines. Operations Research Letters. 28:2001;205-212.
    • (2001) Operations Research Letters , vol.28 , pp. 205-212
    • Baptiste, P.1    Timkovsky, V.G.2
  • 7
    • 4243781951 scopus 로고
    • A polynomial time algorithm for an open shop problem with unit processing times and tree constraints
    • Bräsel H., Kluge D., Werner F. A polynomial time algorithm for an open shop problem with unit processing times and tree constraints. Discrete Applied Mathematics. 59:1995;11-21.
    • (1995) Discrete Applied Mathematics , vol.59 , pp. 11-21
    • Bräsel, H.1    Kluge, D.2    Werner, F.3
  • 8
    • 0037851104 scopus 로고    scopus 로고
    • private communication
    • P. Brucker, private communication.
    • Brucker, P.1
  • 10
    • 0017524635 scopus 로고
    • Scheduling equal-length tasks under tree-like precedence constraints to minimize maximum lateness
    • Brucker P., Garey M.R., Johnson D.S. Scheduling equal-length tasks under tree-like precedence constraints to minimize maximum lateness. Mathematics of Operations Research. 2:1977;275-284.
    • (1977) Mathematics of Operations Research , vol.2 , pp. 275-284
    • Brucker, P.1    Garey, M.R.2    Johnson, D.S.3
  • 14
    • 0037513525 scopus 로고    scopus 로고
    • Complexity results for single-machine problems with positive finish-start time lags
    • Brucker P., Knust S. Complexity results for single-machine problems with positive finish-start time lags. Computing. 63:1999;299-316.
    • (1999) Computing , vol.63 , pp. 299-316
    • Brucker, P.1    Knust, S.2
  • 15
    • 0030125537 scopus 로고    scopus 로고
    • Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems
    • Brucker P., Krämer A. Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems. European Journal of Operational Research. 90:1996;214-226.
    • (1996) European Journal of Operational Research , vol.90 , pp. 214-226
    • Brucker, P.1    Krämer, A.2
  • 16
  • 18
    • 0019563706 scopus 로고
    • Preemptive scheduling of independent jobs with release and due dates on open, flow and job shops
    • Cho Y., Sahni S. Preemptive scheduling of independent jobs with release and due dates on open, flow and job shops. Operations Research. 29:1981;511-522.
    • (1981) Operations Research , vol.29 , pp. 511-522
    • Cho, Y.1    Sahni, S.2
  • 19
    • 0015482117 scopus 로고
    • Optimal scheduling for two-processor systems
    • Coffman E.G. Jr., Graham R.L. Optimal scheduling for two-processor systems. Acta Informatica. 1:1972;200-213.
    • (1972) Acta Informatica , vol.1 , pp. 200-213
    • Coffman E.G., Jr.1    Graham, R.L.2
  • 21
    • 0038527463 scopus 로고
    • A new algorithm for scheduling of tree structured tasks
    • Baltimore, MD
    • G.I. Davida, D.J. Linton, A new algorithm for scheduling of tree structured tasks, in Proc. Conf. Inform. Sci. and Syst., Baltimore, MD, 1976, pp. 543-548.
    • (1976) Proc. Conf. Inform. Sci. and Syst. , pp. 543-548
    • Davida, G.I.1    Linton, D.J.2
  • 23
    • 0000474126 scopus 로고
    • Minimizing total tardiness on one machine is NP-hard
    • Du J., Leung J.Y.-T. Minimizing total tardiness on one machine is NP-hard. Mathematics of Operations Research. 15(3):1990;483-495.
    • (1990) Mathematics of Operations Research , vol.15 , Issue.3 , pp. 483-495
    • Du, J.1    Leung, J.Y.-T.2
  • 24
    • 38249005272 scopus 로고
    • Minimizing mean flow time in two-machine open shops and flow shops
    • Du J., Leung J.Y.-T. Minimizing mean flow time in two-machine open shops and flow shops. Journal of Algorithms. 14:1993;24-44.
    • (1993) Journal of Algorithms , vol.14 , pp. 24-44
    • Du, J.1    Leung, J.Y.-T.2
  • 27
    • 0026170095 scopus 로고
    • Scheduling chain-structured tasks to minimize makespan and mean flow time
    • Du J., Leung J.Y.-T., Young G.H. Scheduling chain-structured tasks to minimize makespan and mean flow time. Information and Computation. 92:1991;219-236.
    • (1991) Information and Computation , vol.92 , pp. 219-236
    • Du, J.1    Leung, J.Y.-T.2    Young, G.H.3
  • 28
    • 0001097778 scopus 로고
    • Two-processor scheduling with start-times and deadlines
    • Garey M.R., Johnson D.S. Two-processor scheduling with start-times and deadlines. SIAM Journal on Computing. 6:1977;416-426.
    • (1977) SIAM Journal on Computing , vol.6 , pp. 416-426
    • Garey, M.R.1    Johnson, D.S.2
  • 30
    • 0031272669 scopus 로고    scopus 로고
    • A two-machine preemptive openshop scheduling problem: An elementary proof of NP-completeness
    • Gladky A.A. A two-machine preemptive openshop scheduling problem: An elementary proof of NP-completeness. European Journal of Operational Research. 103:1997;113-116.
    • (1997) European Journal of Operational Research , vol.103 , pp. 113-116
    • Gladky, A.A.1
  • 31
    • 0019000425 scopus 로고
    • A new algorithm for preemptive scheduling of trees
    • Gonzalez T., Johnson D.B. A new algorithm for preemptive scheduling of trees. Journal of the ACM. 27:1980;287-312.
    • (1980) Journal of the ACM , vol.27 , pp. 287-312
    • Gonzalez, T.1    Johnson, D.B.2
  • 32
    • 0017012325 scopus 로고
    • Openshop scheduling to minimize finish time
    • Gonzalez T., Sahni S. Openshop scheduling to minimize finish time. Journal of the ACM. 23:1976;665-679.
    • (1976) Journal of the ACM , vol.23 , pp. 665-679
    • Gonzalez, T.1    Sahni, S.2
  • 33
    • 0017918132 scopus 로고
    • Flow shop and job shop schedules: Complexity and approximation
    • Gonzalez T., Sahni S. Flow shop and job shop schedules: Complexity and approximation. Operations Research. 26:1978;36-52.
    • (1978) Operations Research , vol.26 , pp. 36-52
    • Gonzalez, T.1    Sahni, S.2
  • 35
    • 0017419682 scopus 로고
    • A level algorithm for preemptive scheduling
    • Horvath E.C., Lam S., Sethi R. A level algorithm for preemptive scheduling. Journal of the ACM. 24:1977;32-43.
    • (1977) Journal of the ACM , vol.24 , pp. 32-43
    • Horvath, E.C.1    Lam, S.2    Sethi, R.3
  • 36
    • 0001430010 scopus 로고
    • Parallel sequencing and assembly line problems
    • Hu T.C. Parallel sequencing and assembly line problems. Operations Research. 9:1961;841-848.
    • (1961) Operations Research , vol.9 , pp. 841-848
    • Hu, T.C.1
  • 37
    • 0003037529 scopus 로고
    • Reducibility among combinatorial problems
    • R.E. Miller, & J.W. Thatcher. New York: Plenum Press
    • Karp R.M. Reducibility among combinatorial problems. Miller R.E., Thatcher J.W. Complexity of Computer Computations. 1972;85-103 Plenum Press, New York.
    • (1972) Complexity of Computer Computations , pp. 85-103
    • Karp, R.M.1
  • 38
    • 0037851100 scopus 로고    scopus 로고
    • A polynomial time algorithm for a two-machine no-wait job-shop scheduling problem
    • Kravchenko S.A. A polynomial time algorithm for a two-machine no-wait job-shop scheduling problem. European Journal of Operational Research. 106:1998;101-107.
    • (1998) European Journal of Operational Research , vol.106 , pp. 101-107
    • Kravchenko, S.A.1
  • 39
    • 0038527464 scopus 로고    scopus 로고
    • On the complexity of minimizing the number of late jobs in unit-time open shop
    • Kravchenko S.A. On the complexity of minimizing the number of late jobs in unit-time open shop. Discrete Applied Mathematics. 100:1999;127-132.
    • (1999) Discrete Applied Mathematics , vol.100 , pp. 127-132
    • Kravchenko, S.A.1
  • 40
    • 0037513522 scopus 로고    scopus 로고
    • Minimizing the number of late jobs for the two-machine unit-time job-shop scheduling problem
    • Kravchenko S.A. Minimizing the number of late jobs for the two-machine unit-time job-shop scheduling problem. Discrete Applied Mathematics. 98(3):1999;209-217.
    • (1999) Discrete Applied Mathematics , vol.98 , Issue.3 , pp. 209-217
    • Kravchenko, S.A.1
  • 41
    • 0037851101 scopus 로고
    • Exact and approximate algorithms for scheduling unit time tasks with tree-like precedence constraints
    • Kubiak W. Exact and approximate algorithms for scheduling unit time tasks with tree-like precedence constraints. Abstracts EURO IX-TIMS XXVIII Paris. 1988;195.
    • (1988) Abstracts EURO IX-TIMS XXVIII Paris , pp. 195
    • Kubiak, W.1
  • 42
    • 0024916622 scopus 로고
    • A pseudopolynomial algorithm for a two-machine no-wait job shop problem
    • Kubiak W. A pseudopolynomial algorithm for a two-machine no-wait job shop problem. European Journal of Operational Research. 43:1989;267-270.
    • (1989) European Journal of Operational Research , vol.43 , pp. 267-270
    • Kubiak, W.1
  • 44
    • 0037851110 scopus 로고
    • A note on the complexity of open shop scheduling problems
    • Kubiak W., Sriskandarajah C., Zaras K. A note on the complexity of open shop scheduling problems. INFOR. 29:1991;284-294.
    • (1991) INFOR , vol.29 , pp. 284-294
    • Kubiak, W.1    Sriskandarajah, C.2    Zaras, K.3
  • 45
    • 0030264824 scopus 로고    scopus 로고
    • A polynomial-time algorithm for total completion time minimization in two-machine job-shop with unit-time operations
    • Kubiak W., Timkovsky V.G. A polynomial-time algorithm for total completion time minimization in two-machine job-shop with unit-time operations. European Journal of Operational Research. 94:1996;310-320.
    • (1996) European Journal of Operational Research , vol.94 , pp. 310-320
    • Kubiak, W.1    Timkovsky, V.G.2
  • 47
    • 77957077792 scopus 로고
    • A 'pseudopolynomial' algorithm for sequencing jobs to minimize total tardiness
    • Lawler E.L. A 'pseudopolynomial' algorithm for sequencing jobs to minimize total tardiness. Annals of Discrete Mathematics. 1:1977;331-342.
    • (1977) Annals of Discrete Mathematics , vol.1 , pp. 331-342
    • Lawler, E.L.1
  • 49
    • 0006998543 scopus 로고
    • Preemptive scheduling of precedence-constrained jobs on parallel machines
    • M.A.H. Dempster, J.K. Lenstra, & A.H.G. Rinnooy Kan. Dordrecht: Reidel
    • Lawler E.L. Preemptive scheduling of precedence-constrained jobs on parallel machines. Dempster M.A.H., Lenstra J.K., Rinnooy Kan A.H.G. Deterministic and Stochastic Scheduling. 1982;101-123 Reidel, Dordrecht.
    • (1982) Deterministic and Stochastic Scheduling , pp. 101-123
    • Lawler, E.L.1
  • 50
    • 0010916439 scopus 로고
    • Recent results in theory of machine scheduling
    • A. Bachem. Bonn
    • Lawler E.L. Recent results in theory of machine scheduling. Bachem A. Mathematical Programming: The State of the Art, Bonn, 1982. 1983;202-234.
    • (1982) Mathematical Programming: The State of the Art , pp. 202-234
    • Lawler, E.L.1
  • 51
    • 0018020599 scopus 로고
    • On preemptive scheduling of unrelated parallel processors by linear programming
    • Lawler E.L., Labetoulle J. On preemptive scheduling of unrelated parallel processors by linear programming. Journal of the ACM. 25:1978;612-619.
    • (1978) Journal of the ACM , vol.25 , pp. 612-619
    • Lawler, E.L.1    Labetoulle, J.2
  • 54
    • 0024628849 scopus 로고
    • Preemptive scheduling of two uniform machines to minimize the number of late jobs
    • Lawler E.L., Martel C.U. Preemptive scheduling of two uniform machines to minimize the number of late jobs. Operations Research. 37:1989;314-318.
    • (1989) Operations Research , vol.37 , pp. 314-318
    • Lawler, E.L.1    Martel, C.U.2
  • 55
    • 0038188834 scopus 로고    scopus 로고
    • private communication
    • J.K. Lenstra, private communication.
    • Lenstra, J.K.1
  • 56
    • 0017924416 scopus 로고
    • Complexity of scheduling under precedence constraints
    • Lenstra J.K., Rinnooy Kan A.H.G. Complexity of scheduling under precedence constraints. Operations Research. 26:1979;22-35.
    • (1979) Operations Research , vol.26 , pp. 22-35
    • Lenstra, J.K.1    Rinnooy Kan, A.H.G.2
  • 61
    • 0037513521 scopus 로고
    • Minimizing total tardiness on a single machine with precedence constraints
    • Leung J.T.-Y., Young G.H. Minimizing total tardiness on a single machine with precedence constraints. ORSA Journal on Computing. 2:1990;346-352.
    • (1990) ORSA Journal on Computing , vol.2 , pp. 346-352
    • Leung, J.T.-Y.1    Young, G.H.2
  • 62
    • 0022101768 scopus 로고
    • On the complexity of preemptive open shop scheduling problems
    • Liu C.Y., Bulfin R.L. On the complexity of preemptive open shop scheduling problems. Operations Research Letters. 4:1985;71-74.
    • (1985) Operations Research Letters , vol.4 , pp. 71-74
    • Liu, C.Y.1    Bulfin, R.L.2
  • 63
    • 0024038037 scopus 로고
    • Scheduling open shops with unit execution times to minimize functions of due dates
    • Liu C.Y., Bulfin R.L. Scheduling open shops with unit execution times to minimize functions of due dates. Operations Research. 36:1988;553-559.
    • (1988) Operations Research , vol.36 , pp. 553-559
    • Liu, C.Y.1    Bulfin, R.L.2
  • 64
    • 0037851099 scopus 로고    scopus 로고
    • Two machine open shop scheduling problem with release dates, unit processing times and precedence constraints
    • Magdeburg
    • I. Lushchakova, Two machine open shop scheduling problem with release dates, unit processing times and precedence constraints, in Book of Abstracts, SOR'99, Magdeburg, 1999, p. 79.
    • (1999) Book of Abstracts, SOR'99 , pp. 79
    • Lushchakova, I.1
  • 65
    • 0004990720 scopus 로고
    • On sequencing n jobs on one machine to minimize the number of late jobs
    • Maxwell W.L. On sequencing. n jobs on one machine to minimize the number of late jobs Management Science. 16:1970;295-297.
    • (1970) Management Science , vol.16 , pp. 295-297
    • Maxwell, W.L.1
  • 66
    • 0002643827 scopus 로고
    • Scheduling with deadlines and loss functions
    • McNaughton R. Scheduling with deadlines and loss functions. Management Science. 6:1959;1-12.
    • (1959) Management Science , vol.6 , pp. 1-12
    • McNaughton, R.1
  • 67
    • 0010737739 scopus 로고    scopus 로고
    • Transversal graphs for partially ordered sets: Sequencing, scheduling and merging problems
    • Middendorf M., Timkovsky V.G. Transversal graphs for partially ordered sets: Sequencing, scheduling and merging problems. Journal of Combinatorial Optimization. 3(4):1999;417-435.
    • (1999) Journal of Combinatorial Optimization , vol.3 , Issue.4 , pp. 417-435
    • Middendorf, M.1    Timkovsky, V.G.2
  • 68
    • 0019896960 scopus 로고
    • Linear-time algorithms for scheduling on parallel processors
    • Monma C.L. Linear-time algorithms for scheduling on parallel processors. Operations Research. 30:1982;116-124.
    • (1982) Operations Research , vol.30 , pp. 116-124
    • Monma, C.L.1
  • 69
    • 0000062028 scopus 로고
    • An n job, one machine sequencing algorithm for minimizing the number of late jobs
    • Moore J.M. An. n job, one machine sequencing algorithm for minimizing the number of late jobs Management Science. 15:1968;102-109.
    • (1968) Management Science , vol.15 , pp. 102-109
    • Moore, J.M.1
  • 70
    • 0014766132 scopus 로고
    • Preemptive scheduling of real time tasks on multiprocessor systems
    • Muntz R.R., Coffman E.G. Jr. Preemptive scheduling of real time tasks on multiprocessor systems. Journal of the ACM. 17:1970;324-338.
    • (1970) Journal of the ACM , vol.17 , pp. 324-338
    • Muntz, R.R.1    Coffman E.G., Jr.2
  • 71
    • 0038188832 scopus 로고
    • Computing the bump number with techniques from two-processor scheduling
    • Schäffer A.A., Simons B. Computing the bump number with techniques from two-processor scheduling. Order. 5:1988;131-141.
    • (1988) Order , vol.5 , pp. 131-141
    • Schäffer, A.A.1    Simons, B.2
  • 72
    • 0038188833 scopus 로고
    • Algorithms for minimal-length schedules
    • E.G. Jr. Coffman. New York: John Wiley
    • Sethi R. Algorithms for minimal-length schedules. Coffman E.G. Jr. Computer and Job-Shop Scheduling Theory. 1976;51-99 John Wiley, New York.
    • (1976) Computer and Job-Shop Scheduling Theory , pp. 51-99
    • Sethi, R.1
  • 73
    • 0000102070 scopus 로고
    • Multiprocessor scheduling of unit-time jobs with arbitrary release times and deadlines
    • Simons B. Multiprocessor scheduling of unit-time jobs with arbitrary release times and deadlines. SIAM Journal on Computing. 12:1983;294-299.
    • (1983) SIAM Journal on Computing , vol.12 , pp. 294-299
    • Simons, B.1
  • 74
    • 0024716133 scopus 로고
    • A fast algorithm for multiprocessor scheduling of unit-length jobs
    • Simons B., Warmuth M. A fast algorithm for multiprocessor scheduling of unit-length jobs. SIAM Journal on Computing. 18:1989;690-710.
    • (1989) SIAM Journal on Computing , vol.18 , pp. 690-710
    • Simons, B.1    Warmuth, M.2
  • 77
    • 0037851097 scopus 로고    scopus 로고
    • Minimizing the total completion time in a unit-time open shop with release times
    • Tautenhahn T., Woeginger G.J. Minimizing the total completion time in a unit-time open shop with release times. Operations Research Letters. 20:1997;207-212.
    • (1997) Operations Research Letters , vol.20 , pp. 207-212
    • Tautenhahn, T.1    Woeginger, G.J.2
  • 79
    • 0005847198 scopus 로고    scopus 로고
    • A polynomial-time algorithm for the two-machine unit-time release-date job-shop schedule-length problem
    • Timkovsky V.G. A polynomial-time algorithm for the two-machine unit-time release-date job-shop schedule-length problem. Discrete Applied Mathematics. 77:1997;185-200.
    • (1997) Discrete Applied Mathematics , vol.77 , pp. 185-200
    • Timkovsky, V.G.1
  • 80
    • 0004708371 scopus 로고    scopus 로고
    • Is a unit-time job shop not easier than identical parallel machines?
    • Timkovsky V.G. Is a unit-time job shop not easier than identical parallel machines? Discrete Applied Mathematics. 85:1998;149-162.
    • (1998) Discrete Applied Mathematics , vol.85 , pp. 149-162
    • Timkovsky, V.G.1
  • 83
    • 0010322740 scopus 로고
    • Complexity of sequencing problems
    • E.G. Jr. Coffman. New York: John Wiley
    • Ullman J.D. Complexity of sequencing problems. Coffman E.G. Jr. Computer and Job-Shop Scheduling Theory. 1976;139-164 John Wiley, New York.
    • (1976) Computer and Job-Shop Scheduling Theory , pp. 139-164
    • Ullman, J.D.1


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