Scheduling nonlinear divisible loads in a single level tree network

In this paper, we study the scheduling problem for polynomial time complexity computational loads in a single level tree network with a collective communication model. The problem of minimizing the processing time is investigated when the computational loads require polynomial order of processing time which is proportional to the size of load fraction. In the divisible load theory framework, the presence of polynomial time complexity computational loads leads to solving higher-order algebraic equations to find the optimal load fractions assigned to the processors in the network. The problem of finding optimal load fraction is a computationally intensive task. Using a mild assumption on the ratio of communication time to computation time, we present a closed-form solution for near optimal load fractions and processing time for the entire load fractions. Finally, we also present a closed-form solution for scheduling polynomial loads with start-up delay in communication and computation. The numerical speedup results obtained using closed-form solution clearly show that super-linear speedup is possible for the polynomial computational loads.