Scheduling with Unit Processing and Communication Times on a Ring Network: Approximation Results

We consider the problem of scheduling UET-UCT task graphs on a ring network of m processors, in order to minimize the makespan. We show that no polynomial-time algorithm with relative performance better than 4/3 can exist in that case (unless P=NP), and prove that the relative performance g of the general list scheduling algorithm proposed by Rayward-Smith is such that [√m]≤g ≲-1 + 3/8m −1/2m, for m even.