We study the unweighted throughput scheduling problem on a single machine in the preemption-revoke model, where a running job may be aborted at any time, but all progress is permanently lost and the job cannot be restarted. Each job $J_i=(r_i,p_i,s_i)$ is defined by a release time $r_i$, a processing time $p_i$, and a slack $s_i$, and must start no later than $r_i+s_i$ to be feasible. We prove that no deterministic online algorithm can achieve a constant competitive ratio. The lower bound is established via an adversarial construction: starting from a three-job instance where $\textsf{ALG}$ completes at most one job while $\textsf{OPT}$ completes all three, we iteratively nest such constructions. By induction, for every $k\ge 3$, there exists an instance where $\textsf{ALG}$ completes at most one job, while $\textsf{OPT}$ completes at least $k$ jobs. Thus, the competitive ratio can be forced to $1/k$, and hence made arbitrarily close to zero. Our result stands in sharp contrast to the preemption-restart model, where Hoogeveen, Potts, and Woeginger (2000) gave a deterministic $1/2$-competitive algorithm.

翻译：我们研究了抢占-撤销模型下单一机器上的无权重吞吐量调度问题，其中正在运行的作业可随时被中止，但所有进度将永久丢失且该作业无法重新启动。每个作业 $J_i=(r_i,p_i,s_i)$ 由释放时间 $r_i$、处理时间 $p_i$ 和松弛时间 $s_i$ 定义，且必须在 $r_i+s_i$ 之前开始执行方为可行。我们证明不存在确定性在线算法能达到常数竞争比。该下界通过对抗性构造建立：从一个三作业实例出发（其中 $\textsf{ALG}$ 至多完成一个作业，而 $\textsf{OPT}$ 完成全部三个作业），我们迭代地嵌套此类构造。通过归纳法可证，对于任意 $k\ge 3$，均存在一个实例使得 $\textsf{ALG}$ 至多完成一个作业，而 $\textsf{OPT}$ 至少完成 $k$ 个作业。因此竞争比可被压低至 $1/k$，从而无限趋近于零。我们的结果与抢占-重启模型形成鲜明对比——Hoogeveen、Potts 和 Woeginger（2000）在该模型中给出了确定性的 $1/2$ 竞争算法。