We consider the competitive multi-agent scheduling problem on a single machine, where each agent’s cost function is to minimize its total weighted late work. The aim is to find the Pareto-optimal frontier, i.e., the set of all Pareto-optimal points. When the number of agents is arbitrary, the decision problem is shown to be unary $$\mathcal {NP}$$ NP -complete even if all jobs have the unit weights. When the number of agents is two, the decision problems are shown to be binary $$\mathcal {NP}$$ NP -complete for the case in which all jobs have the common due date and the case in which all jobs have the unit processing times. When the number of agents is a fixed constant, a pseudo-polynomial dynamic programming algorithm and a $$(1+\epsilon )$$ ( 1 + ϵ ) -approximate Pareto-optimal frontier are designed to solve it.

中文翻译：

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具有多代理的单机调度以最小化总加权延迟工作

我们考虑单台机器上的竞争性多代理调度问题，其中每个代理的成本函数是最小化其总加权延迟工作。目标是找到帕累托最优边界，即所有帕累托最优点的集合。当代理的数量是任意的时，即使所有作业都有单位权重，决策问题也显示为一元 $$\mathcal {NP}$$ NP -complete。当代理的数量为 2 时，对于所有作业具有共同截止日期的情况和所有作业都有单位的情况，决策问题显示为二元的 $$\mathcal {NP}$$ NP -complete处理时间。当代理的数量是固定常数时，设计了一个伪多项式动态规划算法和一个 $$(1+\epsilon )$$ ( 1 + ϵ ) -approximate Pareto-optimal frontier 来解决它。