Abstract
The paper is concerned with the problem of scheduling partially ordered unit execution time tasks on parallel processors with unit communication delays and release times. Two criteria are considered, the maximum lateness and its particular case, the makespan. This problem plays an important role in scheduling theory and was originally inspired by the applications to multi-processor computer systems. It is well known that for both criteria the problem is NP-hard in the strong sense. The paper presents an implementation of the branch-and-bound method which does not partition the feasible region explicitly. The theoretical results are complemented by computational experiments.
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References
Brucker P (2004) Scheduling algorithms, 4th edn. Springer, Berlin
Chrétienne P, Picouleau C (1995) Scheduling with communication delays: a survey. In: Scheduling theory and its applications. Wiley, New York, pp 65–90
Finke G, Gordon V, Proth J (2004) Scheduling with due dates (annotated bibliography of complexity and algorithms). Tech Rep 42, Laboratoire Leibniz-IMAG
Garey M, Johnson D (1976) Scheduling tasks with nonuniform deadlines on two processors. J Assoc Comput Mach 23(3):461–467
Graham R, Lawler E, Lenstra J, Kan AR (1979) Optimization and approximation in deterministic machine scheduling: a survey. Ann Discrete Math 5:287–326
Kowk Y, Ahmad I (1997) Efficient scheduling of arbitrary task graphs to multiprocessors using a parallel genetic algorithm. J Parallel Distrib Comput 47:58–77
Pinedo M (2002) Scheduling: theory, algorithms, and systems. Prentice Hall, New York
Rayward-Smith V (1987) UET scheduling with unit interprocessor communication delays. Discrete Appl Math 18:55–71
Zinder Y (2003) An iterative algorithm for scheduling uet tasks with due dates and release times. Eur J Oper Res 149:404–416
Zinder Y, Roper D (1998) An iterative algorithm for scheduling unit-time tasks with precedence constraints to minimise the maximum lateness. Ann Oper Res 81:321–340
Zinder Y, Singh G, Weiskircher R (2006) A new method of scheduling unit time tasks on parallel machines. In: Lecture notes in engineering and computer science. Springer, Berlin, pp 796–801
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Zinder, Y., Su, B., Singh, G. et al. Scheduling UET-UCT tasks: branch-and-bound search in the priority space. Optim Eng 11, 627–646 (2010). https://doi.org/10.1007/s11081-009-9080-8
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DOI: https://doi.org/10.1007/s11081-009-9080-8