Scheduling Second-Order Computational Load in Master-Slave Paradigm

Scheduling divisible loads with the nonlinear computational complexity is a challenging task as the recursive equations are nonlinear and it is difficult to find closed-form expression for processing time and load fractions. In this study we attempt to address a divisible load scheduling problem for computational loads having second-order computational complexity in a master-slave paradigm with nonblocking mode of communication. First, we develop algebraic means of determining the optimal size of load fractions assigned to the processors in the network using a mild assumption on communication-to-computation speed ratio. We use numerical simulation to verify the closeness of the proposed solution. Like in earlier works which consider processing loads with first-order computational complexity, we study the conditions for optimal sequence and arrangements using the closed-form expression for optimal processing time. Our finding reveals that the condition for optimal sequence and arrangements for second-order computational loads are the same as that of linear computational loads. This scheduling algorithm can be used for aerospace applications such as Hough transform for image processing and pattern recognition using hidden Markov model (HMM).