Abstract
In this paper we study a scheduling problem arising from executing numerical simulations on HPC architectures. With a constant number of parallel machines, the objective is to minimize the makespan under memory constraints for the machines. Those constraints come from a neighborhood graph G for the jobs. Motivated by a previous result on graphs G with bounded path-width, our focus is on the case when the neighborhood graph G has bounded tree-width. Our result is a bi-criteria fully polynomial time approximation algorithm based on a dynamic programming algorithm. It allows to find a solution within a factor of \(1+\epsilon \) of the optimal makespan, where the memory capacity of the machines may be exceeded by a factor at most \(1+\epsilon \). This result relies on the use of a nice tree decomposition of G and its traversal in a specific way which may be useful on its own. The case of unrelated machines is also tractable with minor modifications.
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Notes
- 1.
The neighborhood is most of the time topologically defined (cells sharing an edge or a face).
- 2.
For sake of readability, the result is presented for two machines but it can be extended to any number of machines, as discussed in the conclusion.
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Angel, E., Morais, S., Regnault, D. (2022). A Bi-Criteria FPTAS for Scheduling with Memory Constraints on Graphs with Bounded Tree-Width. In: Cano, J., Trinder, P. (eds) Euro-Par 2022: Parallel Processing. Euro-Par 2022. Lecture Notes in Computer Science, vol 13440. Springer, Cham. https://doi.org/10.1007/978-3-031-12597-3_9
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