On the hardness of approximating the UET-UCT scheduling problem with hierarchical communications

We consider the unit execution time unit communication time (UET-UCT) scheduling model with hierarchical communications, and we study the impact of the hierarchical communications hypothesis on the hardness of approximation. We prove that there is no polynomial time approximation algorithm with performance guarantee smaller than 5/4 (unless P=NP). This result is an extension of the result of Hoogeveen et al. who proved that there is no polynomial time ρ-approximation algorithm with ρ<7/6 for the classical UET-UCT scheduling problem with homogeneous communication delays and an unrestricted number of identical machines.