Abstract
In general, scheduling problems considered in this book are characterized by three sets: set T = {T 1, T 2,…,T n} of n tasks, set P = {P 1, P 2,…,P m} of m processors (machines) and set R = {R 1, R 2,…,R s} of s types of additional resources R. Scheduling, generally speaking, means to assign processors from P and (possibly) resources from R to tasks from T in order to complete all tasks under the imposed constraints. There are two general constraints in classical scheduling theory. Each task is to be processed by at most one processor at a time (plus possibly specified amounts of additional resources) and each processor is capable of processing at most one task at a time. In Sections 5.4 and 7.2 we will show some new applications in which the first constraint will be relaxed.
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References
ACM Record of the project MAC conference on concurrent system and parallel computation, Wood’s Hole, Mass, 1970.
A. V. Aho, J. E. Hopcroft, J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass., 1974.
J. L. Baer, Optimal scheduling on two processors of different speeds, in: E. Gelenbe, R. Mahl (eds.), Computer Architecture and Networks, North Holland, Amsterdam, 1974.
J. Błażewicz, W. Cellary, R. Słowiński, J. Węglarz, Scheduling under Resource Constraints: Deterministic Models, J. C. Baltzer, Basel, 1986.
A. J. Bernstein, Analysis of programs for parallel programming, IEEE Trans. Comput. EC-15, 1966, 757–762.
J. Błażewicz, J. K. Lenstra, A. H. G. Rinnooy Kan, Scheduling subject to resource constraints: classification and complexity, Discrete Appl. Math. 5, 1983, 11–24.
E. G. Coffman, Jr., P. J. Denning, Operating Systems Theory, Prentice-Hall, Englewood Cliffs, N.J., 1973.
S. A. Cook, The complexity of theorem proving procedures, Proc. 3rd ACM Symposium on Theory of Computing, 1971, 151–158.
M. R. Garey, D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco, 1979.
R. L. Graham, E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling theory: a survey, Ann. Discrete Math. 5, 1979, 287–326.
R. M. Karp, Reducibility among combinatorial problems, in: R. E. Miller, J. W. Thatcher (eds.), Complexity of Computer Computations, Plenum Press, New York, 1972, 85–104.
C. V. Ramamoorthy, M. J. Gonzalez, A survey of techniques for recognizing parallel processable streams in computer programs, AFIPS Conference Proceedings, Fall Joint Computer Conference, 1969, 1–15.
E. C. Russel, Automatic program analysis, Ph.D. thesis, Dept. of Eng. University of California, Los Angeles, 1969.
S. Volansky, Graph model analysis and implementation of computational sequences Ph.D. thesis, Rep. No.UCLA-ENG-7048, School of Engineering Applied Sciences, University of California, Los Angeles, 1970.
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© 1994 Springer-Verlag Berlin · Heidelberg
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Błazewicz, J., Ecker, K.H., Schmidt, G., Węglarz, J. (1994). Formulation of Scheduling Problems. In: Scheduling in Computer and Manufacturing Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79034-8_3
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DOI: https://doi.org/10.1007/978-3-642-79034-8_3
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