Scheduling chains on Uniform Processors with Communication Delays

Wieslaw Kubiak (1) , Bernard Penz (2) , Denis Trystram (1, 3, 4, 5)

1 APACHE - Parallel algorithms and load sharing
2 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
3 ID-IMAG - Informatique et Distribution
4 LMC - IMAG - Laboratoire de Modélisation et Calcul
5 MOAIS - PrograMming and scheduling design fOr Applications in Interactive Simulation

We show that the problem of scheduling chains of unit execution time (UET) jobs on uniform processors with communication delays to minimize makespan is NP-hard in the strong sense. We also give a heuristic that generates solutions with known, and relatively small, absolute error for this problem. The NP-hardness result holds even for the case without communication delays, and complements the earlier result of Gonzalez and Sahni who gave a polynomial time algorithm for preemptive jobs of arbitrary length.
We also study the structure of optimal solutions for the two processor problem of scheduling chains of UET jobs with communication delays, where one processor is a (integer) times faster than the other. This investigation leads to a linear time optimization algorithm for this case.

Domaines: Recherche opérationnelle [math.OC]

Wieslaw Kubiak, Bernard Penz, Denis Trystram. Scheduling chains on Uniform Processors with Communication Delays. Journal of Scheduling, 2002, 4, pp.459 - 476. ⟨10.1002/jos.121⟩. ⟨hal-00239332⟩