关于划分DAG任务以最小化能耗的复杂度研究
On the Complexity of Minimizing Energy Consumption of Partitioning DAG Tasks
AI总结：
本文研究DAG任务划分到异构机器的最小能耗问题，证明其为NP难，给出两台机器及DAG为有向路径情形的多项式算法，并证明带单台任务数限制的双机变体仍难解。
摘要：
我们研究一类图划分问题：给定一个有向无环图（DAG），其顶点和弧可分别视为任务以及任务间的依赖关系。该问题的目标是将任务分配到k台异构机器上，以最小化完成这些任务消耗的总能耗。我们首先证明该问题是NP难的。随后，我们针对两种特殊情形给出多项式时间算法，分别是仅存在两台机器的情形，以及输入DAG为有向路径的情形。最后，我们研究了一个自然的问题变体：仅存在两台机器，且其中一台机器可执行的任务数量受限。我们证明该特殊情形在计算上仍然是难解的。
英文摘要：
We study a graph partition problem where we are given a directed acyclic graph (DAG) whose vertices and arcs can be respectively regarded as tasks and dependencies among tasks. The objective of the problem is to minimize the total energy consumed for completing these tasks by assigning the tasks to k heterogeneous machines. We first show that the problem is NP-hard. Then, we present polynomial-time algorithms for two special cases where there are only two machines and where the input DAG is a directed path. Finally, we study a natural variant where there are only two machines with one of them being capable of executing a limited number of tasks. We show that this special case remains computationally hard.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
