%0 Unpublished work %T A Bi-Criteria FPTAS for Scheduling with Memory Constraints on Graphs with Bounded Tree-width %+ Informatique, BioInformatique, Systèmes Complexes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