A Bi-Criteria FPTAS for Scheduling with Memory Constraints on Graphs with Bounded Tree-width

Eric Angel (1) , Sébastien Morais (2, 3) , Damien Regnault (1)

1 IBISC - Informatique, BioInformatique, Systèmes Complexes
2 LIHPC - Laboratoire en Informatique Haute Performance pour le Calcul et la simulation
3 DAM/DIF - DAM Île-de-France

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 +  of the optimal makespan, where the memory capacity of the machines may be exceeded by a factor at most 1 + . 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.

Domains: Computer Science [cs]

Eric Angel, Sébastien Morais, Damien Regnault. A Bi-Criteria FPTAS for Scheduling with Memory Constraints on Graphs with Bounded Tree-width. 2022. ⟨cea-03578940⟩