We study kill-and-restart and preemptive strategies for the fundamental scheduling problem of minimizing the sum of weighted completion times on a single machine in the non-clairvoyant setting. First, we show a lower bound of~$3$ for any deterministic non-clairvoyant kill-and-restart strategy. Then, we give for any $b > 1$ a tight analysis for the natural $b$-scaling kill-and-restart strategy as well as for a randomized variant of it. In particular, we show a competitive ratio of $(1+3\sqrt{3})\approx 6.197$ for the deterministic and of $\approx 3.032$ for the randomized strategy, by making use of the largest eigenvalue of a Toeplitz matrix. In addition, we show that the preemptive Weighted Shortest Elapsed Time First (WSETF) rule is $2$-competitive when jobs are released online, matching the lower bound for the unit weight case with trivial release dates for any non-clairvoyant algorithm. Using this result as well as the competitiveness of round-robin for multiple machines, we prove performance guarantees $<10$ for adaptions of the $b$-scaling strategy to online release dates and unweighted jobs on identical parallel machines.

翻译：首先,我们为任何非clairvoyant的确定性非clairvoyant杀和重新开始战略展示了低于3美元的约束值。然后,我们为天然的美元降价缩放缩缩放第一时间(WSETF)规则提供了任何强力分析。特别是,我们展示了确定性(1+3\sqrt{3})\ approx 6.197美元和随机战略的3.032美元的竞争比重,使用托普利茨矩阵的最大值。此外,我们显示,当工作在网上发布时,先发制最短的缩放电时间(WSETF)规则具有2美元的竞争比重,将单位重量的较低约束比重与任何非clairvoyant $的轻放电日期匹配。我们用这一结果来调整机器的双向正值平方 10 算。