On the complexity of minimizing energy consumption of partitioning DAG tasks

Abstract

We study a graph partition problem where the input is a directed acyclic graph (DAG) representing tasks as vertices and dependencies between tasks as arcs. The goal is to assign the tasks to k heterogeneous machines in a way that minimizes the total energy consumed for completing the tasks. We first show that the problem is NP-hard. Then, we present polynomial-time algorithms for two special cases: one where there are only two machines, and another where the input DAG is a directed path. Finally, we examine a variant where there are only two machines, with one capable of executing a limited number of tasks, and demonstrate that this special case remains computationally hard.