Approximation algorithms for scheduling trees with general communication delays
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+?), where ? 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+?)) and that this bound is tight.
scheduling general communication delays task duration makespan