%0 Unpublished work
%T A Bi-Criteria FPTAS for Scheduling with Memory Constraints on Graphs with Bounded Tree-width
%+ Informatique, BioInformatique, Systèmes Complexes (IBISC)
%+ Laboratoire en Informatique Haute Performance pour le Calcul et la simulation (LIHPC)
%+ DAM Île-de-France (DAM/DIF)
%A Angel, Eric
%A Morais, Sébastien
%A Regnault, Damien
%8 2022
%D 2022
%Z Computer Science [cs]Preprints, Working Papers, ...
%X 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.
%G English
%2 https://cea.hal.science/cea-03578940/document
%2 https://cea.hal.science/cea-03578940/file/main.pdf
%L cea-03578940
%U https://cea.hal.science/cea-03578940
%~ CEA
%~ UNIV-EVRY
%~ IBISC
%~ DAM
%~ CEA-UPSAY
%~ UNIV-PARIS-SACLAY
%~ UNIV-EVRY-SACLAY
%~ UNIVERSITE-PARIS-SACLAY
%~ GS-ENGINEERING
%~ GS-COMPUTER-SCIENCE
%~ GS-LIFE-SCIENCES-HEALTH