References
A.V. Aho, J.E. Hopcroft and J.D. Ullman,The Design and Analysis of Computer Algorithms (Addison-Wesley, Reading, Mass., 1974).
K.R. Baker,Introduction to Sequencing and Scheduling (J. Wiley & Sons, New York, 1974).
J. Błażewicz, Scheduling dependent tasks with different arrival times to meet deadlines, in: E. Gelenbe, H. Beilner (eds.),Modelling and Performance Evaluation of Computer Systems (North-Holland, Amsterdam, 1976) pp. 57–65.
J. Błażewicz, Simple algorithms for multiprocessor scheduling to meet deadlines, Information Processing Letters 6, No. 3 (1977)162–164.
J. Błażewicz, Scheduling with deadlines and resource constraints, Report, Instytut Automatyki, Politechnika Poznańska, 1977.
J. Błażewicz, Complexity of computer scheduling algorithms under resource constraints, Proc. I Meeting AFCET-SMF on Applied Mathematics, Palaiseau (France), 1978, pp. 169–178.
J. Błażewicz, Scheduling tasks on parallel processors under resource constraints to minimize mean finishing time, Methods of Operations Research, No. 35(1979) pp. 67–72.
J. Błażewicz, Złożoność obliczeniowa algorytmów i problemów szeregowania zadań, Wyd. Politechniki Poznańskiej, Seria Rozprawy, No. 104, 1979.
J. Błażewicz, Deadline scheduling of tasks with ready times and resource constraints, Information Processing Letters 8, No. 2 (1979) pp. 60–63.
J. Błażewicz, Solving the resource constrained deadline scheduling problem via reduction to the network flow problem, European J. of Operational Research 6, No. 1 (1981) 75–79.
J. Błażewicz, Selected topics in scheduling theory, in: G. Laporte, S. Martello, M. Minoux, C. Ribeiro (eds.),Annals of Discrete Mathematics (North Holland, Amsterdam) to appear.
J. Błażewicz, J. Barcelo, W. Kubiak, H. Röck, Scheduling tasks on two processors with deadlines and additional resources, European J. of Operational Res., to appear.
J. Błażewicz, W. Cellary, R. Błowiński and J. Węglarz, Deterministyczne problemy szeregowania zadań na równoległych procesorach. Cz.I. Zbiory zadań niezależnych, Podstawy Sterowania 6, No. 2 (1976) 155–178.
J. Błażewicz, W. Cellary and J. Węglarz, A strategy for scheduling splittable tasks to reduce schedule length, Acta Cybernetica 3, No. 2 (1977)99–106.
J. Błażewicz and K. Ecker, A linear time algorithm for restricted bin packing and scheduling problems, Operations Research Letters 2(1983)80–83.
J. Błażewicz, W. Kubiak, H. Röck and J. Szwarcfiter, Minimizing mean flow time under resource constraints on parallel processors (1986) to appear.
J. Błażewicz, J.K. Lenstra and A.H.G. Rinnooy Kan, Scheduling subject to resource constraints; classification and complexity, Discrete Applied Mathematics 5, No. 1 (1983)11–24.
P.J. Brucker, Sequencing unit-time jobs with treelike precedence on machines to minimize maximum lateness, Proc. IX International Symposium on Mathematical Programming, Budapest, 1976.
P. Brucker, M.R. Garey and D.S. Johnson, Scheduling equal-length tasks under treelike precedence constraints to minimize maximum lateness, Mathematics of Operations Research 2(1977)275–284.
J. Bruno, E.G. Coffman, Jr. and R. Sethi, Scheduling independent tasks to reduce mean finishing time, Comm. ACM 17, No. 7 (1974)382–387.
J. Brzeziński, Preemptive scheduling of processors with private memories, Foundations of Control Engineering 5, No. 2 (1980)55–69.
E.G. Jr. Coffman (ed.),Computer & Job/Shop Scheduling Theory (J. Wiley, New York, 1976).
E.G. Jr. Coffman and R.L. Graham, Optimal scheduling for two processors systems, Acta Informatica 1, No. 3 (1972)200–213.
R.W. Conway, W.L. Maxwell and L.W. Miller,Theory of Scheduling (Addison-Wesley, Reading, Mass, 1967).
D.F. Cooper, A note on serial and parallel heuristic for resource-constrained project scheduling, Foundations of Control Engineering 2, No. 2 (1977)131–134.
E.W. Davis, Project scheduling under resource constraints; historical review and categorization of procedures, AIIE Transactions 5(1973)297–313.
S. Even,Graph Algorithms (Computer Science Press Inc, 1979).
A. Federgruen and H. Groenevelt, Preemptive scheduling of uniform machines by ordinary network flow techniques, to appear.
L.R. Ford, Jr. and D.R. Fulkerson,Flows in Networks (Princeton, New Jersey, 1962).
P. Gaćs and L. Lovasz, Khachian's algorithm for linear programming, Report, Computer Science Department, Stanford University, 1979.
Z. Galil and A. Naamad, Network flow and generalized path compression, Proc. ACM Symp. Theory of Comput. 1979, pp. 13–26.
M.R. Garey, unpublished result.
M.R. Garey and R.L. Graham, Bounds for multiprocessor scheduling with resource constraints, SIAM J. on Computing 4(1975)187–200.
M.R. Garey, R.L. Graham, D.S. Johnson and A.C.-C. Yao, Resource constrained scheduling as generalized bin packing, J. Combinatorial Theory Ser. A 21(1976)257–298.
M.R. Garey and D.S. Johnson, Complexity results for multiprocessor scheduling under resource constraints, SIAM J. on Computing 4(1975)397–411.
M.R. Garey and D.S. Johnson, Scheduling tasks with nonuniform deadlines on two processors, J. ACM 23, No. 3 (1976)461–467.
M.R. Garey and D.S. Johnson, Two-processor scheduling with start times and deadlines, SIAM J. on Computing 6(1977)416–426.
M.R. Garey and D.S. Johnson, ‘Strong’ NP-completeness results: motivation, examples and implication, J. ACM 25, No. 4 (1978)499–508.
M.R. Garey and D.S. Johnson, Approximation algorithms for combinatorial problems: an annotated bibliography, in: J.F. Traub (ed.),Algorithms and Complexity: New Directions and Recent Results (Academic Press, New York, 1976) pp. 41–52.
M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman, San Francisco, 1979).
M.R. Garey, D.S. Johnson, B.B. Simons and R.E. Tarjan, Scheduling unit-time tasks with arbitrary release times and deadlines, SIAM J. Comput. 10(1981)256–269.
T. Gonzalez, Optimal mean finish time preemptive schedules, Technical Report 220, Computer Science Department, Pennsylvania State University, 1977.
T. Gonzalez and D.B. Johnson, A new algorithm for preemptive scheduling of trees, J. ACM 27(1980)287–312.
T. Gonzalez, E.L. Lawler and S. Sahni, Optimal preemptive scheduling of a fixed number of unrelated processors in linear time, to appear.
T. Gonzalez and S. Sahni, Preemptive scheduling of uniform processor systems, J. ACM 25, No. 1 (1978)91–101.
R.L. Graham, E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling theory: a survey, Ann. Discrete Math. 5(1979)287–326.
W.A. Horn, Single — machine job sequencing with treelike precedence ordering and linear delay penalties, SIAM J. on Appl. Math. 23(1972)189–202.
W.A. Horn, Minimizing average flow time with parallel machines, Operations Research 21(1973)846–847.
W.A. Horn, Some simple scheduling algorithms, Naval Res. Logist, Quart. 21(1974)177–185.
E. Horowitz and S. Sahni, Exact and approximate algorithms for scheduling non-identical processors, J. ACM 23(1976)317–327.
T.C. Hu, Parallel sequencing and assembly line problems, Operations Research 9, No. 6 (1961)841–848.
J.R. Jackson, Scheduling a production line to minimize maximum tardiness, Research Report 43, Management Science Research Project, University of California, Los Angeles.
D.G. Kafura and V.Y. Shen, Task scheduling on a multiprocessor system with independent memories, SIAM J. Comput. 6(1977)167–187.
O. Kariv and S. Even, An O(n 2.5) algorithm for maximum matching in general graphs, 16-th Annual Symp. on Foundations of Computer science, IEEE (1975)100–112.
R.M. Karp, Reducibility among combinatorial problems, in: R.E. Miller and J.W. Thatcher (eds.)Complexity of Computer Computation (Plenum Press, New York, 1972) pp. 85–104.
R.M. Karp, J.K. Lenstra, C.J.H. McDiarmid and A.H.G. Rinnooy Kan, Probabilistic analysis of combinatorial algorithms: an annotated bibliography, in: M. O'hEigeartaigh, J.K. Lenstra and A.H.G. Rinnooy Kan (eds.),Combinatorial Optimization: Annotated Bibliographies (J. Wiley, Chichester, 1984).
A.W. Karzanov, Determining the maximal flow in a network by the method of preflows, Soviet Math. Dokl. 15(1974)434–437.
L.G. Khachian, A polynomial algorithm for linear programming (in Russian), Doklady Akad. Nauk USSR 244(1979)1093–1096.
K.L. Krause, V.Y. Shen and H.D. Schwetman, Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems, J. ACM 22(1975)522–550, Erratum: J. ACM 24(1977)527.
J. Labetoulle, Some theorems on real time scheduling, in: E. Gelenbe and R. Mahl (eds.)Computer Architecture and Networks, (North-Holland, Amsterdam, 1974) pp. 285–298.
J. Labetoulle, E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy Kan, Preemptive scheduling of uniform machines subject to release dates, in:Progress in Combinatorial Optimization (Academic Press, Toronto, 1984) pp. 245–261.
B.J. Lageweg, unpublished.
B.J. Lageweg, J.K. Lenstra and A.H.G. Rinnooy Kan, Minimizing maximum lateness on one machine: computational experience and some applications, Statistica Neerlandica 30, No. 1 (1976)25–41.
T.H. Lai and S. Sahni, Preemptive scheduling of multiprocessor system with memories to minimizeL max, Technical Report 81-20, Comput. Sci. Dept., University of Minnesota, 1981.
E.L. Lawler, Optimal sequencing of a single machine subject to precedence constraints, Management Sci, 19(1973)544–546.
E.L. Lawler,Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, New York, 1976).
E.L. Lawler, Sequencing jobs to minimize total weighted completion time subject to precedence constraints, Ann. Discrete Math. 2 (1978) 75–90.
E.L. Lawler, Preemptive scheduling of precedence constrained jobs on parallel machines, in: M.A.H. Dempster, J.K. Lenstra and A.H.G. Rinnooy Kan (eds.),Deterministic and Stochastic Scheduling (Reidel, Dordrecht, 1982) pp. 101–123.
E.L. Lawler, Recent results in the theory of machine scheduling in: A. Bachem, M. Grötschel and B. Korte (eds.),Mathematical Programming: The State of the Art-Bonn 1982 (Springer Verlag, Berlin, 1982) pp. 202–234.
E.L. Lawler, unpublished.
E.L. Lawler, J. Labetoulle, Preemptive scheduling of unrelated parallel processors by linear programming, J. ACM 25 (1978) 512–619.
E.L. Lawler, J.K. Lenstra and A.H.G. Rinnooy Kan, Recent developments in deterministic sequencing and scheduling: a survey in: M.A.H. Dempster, J.K. Lenstra, A.H.G. Rinnooy Kan (eds.)Deterministic and Stochastic Scheduling (Reidel, Dordrecht, 1982) pp. 35–73.
E.L. Lawler and J.M. Moors, A functional equation and its application to resource allocation and scheduling problems, Management Sci. 16, No. 1 (1969), 77–84.
H.W. Lenstra, Jr., Integer programming with a fixed number of variables, Report, University of Amsterdam, 1981.
J.K. Lenstra, unpublished.
J.K. Lenstra, Sequencing by Enumerative Methods, Mathematical Centre Tracts 69, Mathematisch Centrum, Amsterdam, 1976.
J.K. Lenstra and A.H.G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res. 25 (1978), 22–35.
J.K. Lenstra and A.H.G. Rinnooy Kan, Scheduling theory since 1981: an annotated bibliography, in: M. O'hEigeartaigh, J.K. Lenstra, A.H.G. Rinnooy Kan (eds.),Combinatorial Optimization: Annotated Bibliographies (J. Wiley, Chichester, 1984).
J.K. Lenstra, A.H.G. Rinnooy Kan and P. Brucker, Complexity of machine scheduling problems, Ann. Discrete Math. 1(1977)343–362.
J.Y.-T. Leung, Bounds on list scheduling of UET tasks with restricted resource constraints, Information Processing Letters 9, No. 4 (1979)167–170.
C.L. Liu and J.W. Layland, Scheduling algorithms for multiprogramming in a hard-real-time environment, J. ACM 20, No. 1 (1973)46–61.
E.L. Lloyd, Scheduling task systems with resources, MIT Laboratory for Computer Science, Tech. Report No. 236, 1980.
E.L. Lloyd, List scheduling bounds for UET system with resources, Information Processing Letters 10, No. 1 (1980)28–31.
E.L. Lloyd, Coffman-Graham scheduling of UET task systems with 0–1 resources, Information Processing Letters 12, No. 1 (1981) pp. 40–45.
R. McNaughton, Scheduling with deadlines and loss functions, Management Sci. 12, No. 1 (1959)1–12.
R.R. Muntz and E.G. Coffman, Jr., Optimal preemptive scheduling on two-processor systems, IEEE Trans. Computers C-18, No 11 (1969) 1014–1020.
R.R. Muntz and E.G. Coffman, Jr., Optimal preemptive scheduling of real time tasks on multiprocessor systems, J. ACM 17, No. 2 (1970)324–328.
A.H.G. Rinnooy Kan, Private communication.
A.H.G. Rinnooy Kan,Machine Scheduling Problems; Classification Complexity and Computations (Nijhoff, The Hague, 1976).
A.H.G. Rinnooy Kan, Probabilistic analysis of approximation algorithms, in: G. Laporte, S. Martello, M. Minoux, C. Ribeiro, (eds.)Annals of Discrete Mathematics (North-Holland, Amsterdam) to appear.
L. Rosenfeld, unpublished result.
S. Sahni and Y. Cho, Nearly on line scheduling of uniform processor system with release times, SIAM J. Comput. 8(1979)275–285.
S. Sahni and Y. Cho, Scheduling independent tasks with due times on a uniform processor system, J. ACM 27(1980)550–563.
S. Sahni and T. Gonzalez, P-complete approximation problems, J. ACM 23(1976)555–565.
T.J. Schaefer, Private communication to M.R. Garey and D.S. Johnson, 1974.
R. Sethi, On the complexity of mean flow time scheduling, Math. Oper. Res. 2(1977)320–330.
J.B. Sidney, Decomposition algorithms for single-machine sequencing with precedence relations and deferral costs, Operations Res. 23(1975)283–298.
E.A. Silver, R.V. Vidal and D. de Werra, A tutorial on heuristic methods, European J. of Oper. Res. 5(1980)153–162.
B. Simons, A fast algorithm for single processor scheduling, Proc. 19th Ann. Symp. on Foundations of Computer Science, IEEE Computer Society, Long Beach, CA, 1978, pp. 246–252.
B. Simons, A fast algorithm for multiprocessor scheduling Proc. 21st Annual IEEE Symp. Foundations of Computer Science, 1980, pp. 50–53.
L. Słomiński, Probabilistic analysis of combinatorial algorithm a bibliography with selected annotation, Computing 28(1982)257–267.
R. Słowiński, Two approaches to problems of resource allocation among project activities — a comparative study. J. Opl. Res. Soc. 31, No. 8 (1980)711–723.
R. Słowiński, Allocation de resources limitées parmi des tâches exécutées par un ensemble de machines indépendantes, in: M. Pelegrin and J. Delmas (eds.),Comparison of Automatic Control and Operational Research Techniques Applied to Large Systems Analysis and Control (Pergamon Press, Oxford, 1979) pp. 189–195.
R. Słowiński, Optimal and heuristic procedures for project scheduling with multiple constrained resource — a survey, Foundations of Control Engineering 2, No. 1 (1977)33–40.
R. Słowiński, L'ordonnancement des tâches préemtives sur les procedures indépendants en présence de ressources supplémentaires, R.A.I.R.O. Informatique Computer Science 15, No. 2 (1981)155–166.
J.D. Ullman, NP-complete scheduling problems, J. Comput. System Sci. 10(1975)384–393.
J.D. Ullman, Complexity of sequencing problems, chapter 4, in [22], 1976.
J. Węglarz, J. Błażewicz, W. Cellary and R. Słowiński, An automatic revised simplex method for constrained resource network scheduling, ACM Trans. on Mathematical Software 3, No. 3 (1977)295–300.
D. de Werra, Preemptive scheduling, linear programming and network flows, SIAM J. Algebraic Discrete Math. 5(1984)11–20.
W.A. Wulf and C.G. Bell, C.mmp- a multi-mini-processor, Proc. FJJC (1972)766–778.
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Chapter 2 parallel machines — Efficient algorithms, complexity results. Ann Oper Res 7, 9–98 (1986). https://doi.org/10.1007/BF02186434
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DOI: https://doi.org/10.1007/BF02186434