发表机构
Washington University in St. Louis; University of Michigan（华盛顿大学圣路易斯分校; 密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对并行作业在线调度问题，证明非先知算法的竞争比下界为Ω(min{m, OPT})，并设计出结合FIFO与Small-Frontier-First的渐近最优非先知算法。
AI 中文摘要
我们研究在m个相同处理器上并行作业的在线调度问题，目标是最小化最大流时间。每个到达的作业由一个有向无环图（DAG）表示，其顶点为单位时间子作业，边指定 precedence 约束。我们考虑非先知算法：作业到达时未知其DAG，且仅当子作业就绪时才被揭示。Agrawal、Moseley、Newman和Pruhs（SPAA 2024）证明，即使每个作业都是出树，先进先出（FIFO）算法的竞争比也为Ω(log m)；他们还证明FIFO在若干自然场景下是O(log m)竞争的，并询问该保证是否扩展到一般实例，更广泛地，是否存在任何非先知算法能达到O(1)竞争。我们通过证明每个非先知在线算法的下界为Ω(min{m, OPT})，其中OPT是最优离线调度的最大流时间，否定了这两个问题的答案。特别地，当OPT≥m时，每个非先知算法在某些实例上的竞争比为Ω(m)，且该下界即使在每个作业都是出森林时也成立。我们用一个渐近最优的非先知算法补充这些下界：FIFO是O(m)竞争的，但即使OPT=O(1)，其竞争比也可达Ω(m)；针对OPT较小的实例，我们设计了Small-Frontier-First算法，其竞争比为O(OPT)，结合两种算法得到竞争比为O(min{m, OPT})的非先知算法。
英文摘要
We study online scheduling of parallel jobs on $m$ identical processors to minimize maximum flow time. Each arriving job is represented by a directed acyclic graph (DAG) whose vertices are unit-time subjobs and whose edges specify precedence constraints. We consider non-clairvoyant algorithms: the DAG is not known when a job arrives, and each subjob is revealed only when it becomes ready. Agrawal, Moseley, Newman, and Pruhs (SPAA 2024) showed that First-In-First-Out (FIFO) has competitive ratio $Ω(\log m)$ even when every job is an out-tree. They also proved that FIFO is $O(\log m)$-competitive in several natural settings and asked whether this guarantee extends to general instances. More broadly, they asked whether any non-clairvoyant algorithm can be $O(1)$-competitive. We answer both questions in the negative by proving a lower bound of $Ω(\min\{m,\mathrm{OPT}\})$ for every non-clairvoyant online algorithm, where $\mathrm{OPT}$ is the maximum flow time of an optimal offline schedule. In particular, every non-clairvoyant algorithm has competitive ratio $Ω(m)$ on some instance with $\mathrm{OPT} \ge m$. The lower bound holds even when every job is an out-forest. We complement these lower bounds with an asymptotically optimal non-clairvoyant algorithm. FIFO is $O(m)$-competitive, but can have competitive ratio $Ω(m)$ even when $\mathrm{OPT}=O(1)$. For instances with small $\mathrm{OPT}$, we design a Small-Frontier-First algorithm that is $O(\mathrm{OPT})$-competitive. Combining the two algorithms yields an $O(\min\{m,\mathrm{OPT}\})$-competitive non-clairvoyant algorithm.
