AI 中文总结
研究非先知调度中随机信号的在线调度问题，设计新算法使竞争比严格低于2，证明新黑箱定理，结果显示随机先知模型能带来改进，为在线算法最坏情况分析指明新方向并架起相关模型间的桥梁。
AI 中文摘要
非先知调度是一种基本的在线模型，调度器最初不知道处理时间。对于总完成时间和完工时间等重要目标，最坏情况分析给出的保证很悲观。近期工作引入了$\varepsilon$-先知模型，即当作业剩余$\varepsilon$部分时调度器收到信号。但现有算法和分析依赖信号时间精确，这在任务分析等应用中难以成立。我们引入随机先知模型，作业执行中会发出随机定时信号。我们设计了新的在线调度算法，其竞争比严格低于2。还证明了新的黑箱定理，通过连续摊还收费论证将预期成对作业延迟的界限转换为竞争保证。结果表明随机先知模型不仅有趣，还能在不同调度目标和机器环境中带来稳健改进，为在线算法的最坏情况分析指明新方向，在学习增强算法和随机信息模型间架起桥梁。
英文摘要
Nonclairvoyant scheduling is a fundamental online model in which processing times are initially unknown to the scheduler. Unfortunately, for important objectives such as total completion time and makespan, worst-case analysis yields pessimistic guarantees: every nonclairvoyant algorithm has a competitive ratio of at least $2$ for these objectives. Recent work introduced $\varepsilon$-clairvoyance, where a scheduler receives a signal once an $\varepsilon$-fraction of a job remains (FOCS'25, NeurIPS'25). This model avoids giving the algorithm a priori predictions as done in learning-augmented algorithms, a practice that is often hard to justify in practice. However, existing algorithms and analyses rely crucially on signal times being precise, an assumption hardly justifiable in applications such as task profiling. We introduce stochastic clairvoyance, a beyond-worst-case model in which each job emits a randomly timed signal during its execution, drawn from a distribution over its processing length. For this model, we design new online scheduling algorithms whose competitive ratios are strictly below $2$ for minimizing total completion time and makespan. On the technical side, we prove a new black-box theorem that converts bounds on expected pairwise job delays into competitive guarantees via a continuous amortized charging argument. Our results show that stochastic clairvoyance is not merely a curiosity: it yields robust improvements across different scheduling objectives and machine environments. More broadly, stochastic clairvoyance suggests a new direction in beyond-worst-case analysis for online algorithms, and builds a bridge between learning-augmented algorithms and stochastic information models.
