FPT approximation algorithm for scheduling with memory constraints

Eric Angel (1) , Cédric Chevalier (2) , Franck Ledoux (2) , Sébastien Morais (1, 2) , Damien Regnault (1)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 DAM/DIF - DAM Île-de-France

In this paper we study a scheduling problem motivated by performing intensive numerical simulations on large meshes. In order to run the simulation as fast as possible, we must allocate computations on different processors such that the makespan is minimized, but also take care of the limited memory on each processor. We present a dynamic programming based algorithm that ensures that both of these objectives are satisfied, within a ratio of 1 + ε. Our algorithm is fixed-parameter tractable (FPT) with respect to the path-width of the graph. For sake of readability, the algorithm is presented for two identical machines, but it can be generalized for a fixed number of unrelated processors.

Mots clés: Approximation algorithm; Dynamic programming; Fixed-parameter tractable; Scheduling

Domaines: Recherche opérationnelle [math.OC]

Eric Angel, Cédric Chevalier, Franck Ledoux, Sébastien Morais, Damien Regnault. FPT approximation algorithm for scheduling with memory constraints. 22nd International Conference on Parallel and Distributed Computing (Euro-Par 2016), Aug 2016, Grenoble, France. pp.196--208, ⟨10.1007/978-3-319-43659-3_15⟩. ⟨hal-01367737⟩