Task Assignment with Precedence Constraint over Networks: A Case Study of Computation-Communication Convergence

We study the task assignment problem of an application composed of multiple tasks in a general heterogeneous processor network or network with computing nodes, considering both the communication delay between processors and the precedence constraints between tasks. The problem of scheduling tasks over the network to minimize total application runtime is formulated, which is shown to be a NP-hard mixed integer program. To solve it, we propose a heuristic algorithm called Binary Relaxation and Discretization Heuristic (BRDH) which is conducted in two steps. First, we obtain a binary-relaxed version of the original problem, and then, we recover the discrete value of the original problem by task sorting. Through simulations, we show the impacts of task number, processor number and communication delay on the total application runtime. Furthermore, through comparison with traditional entire application offloading strategies widely used in current cloud computing and edge computing, our distributed computation offloading strategy shows significant advantage.