Approximation algorithms for scheduling trees with general communication delays

Alix Munier (1)

1 SYSDEF - Systèmes d'aide à la décision et à la formation

We consider the problem of scheduling a tree with general communication delays. Jakoby and Reischuk proved that this problem is NP-hard for binary trees and unlimited number of processors. Firstly, we develop a clustering procedure based on the same lower bounds as Papadimitriou and Yannakakis for a related problem. We deduce an approximation algorithm for an unlimited number of processors with relative performance $2-1/(1+\rho)$, where $\rho$ denotes the maximum ratio between communication delays and duration of tasks. We also prove that, for a limited number of identical processors $m$, any list schedule using the clusters structure has a relative performance bounded by $1+(1-1/m)(2-1/(1+\rho))$ and that this bound is tight.

Domaines: Informatique [cs]

Alix Munier. Approximation algorithms for scheduling trees with general communication delays. Parallel Computing, 1999, 25 (1), pp.41-48. ⟨10.1016/S0167-8191(98)00101-X⟩. ⟨hal-01195665⟩