论文标题
部分可观测时空混沌系统的无模型预测
Online Two-Dimensional Vector Packing with Advice
论文作者
论文摘要
我们考虑在线二维矢量包装问题，显示了该问题的任何{\ sc anyfit}策略的竞争比率的$ 11/5 $的下限。我们提供具有竞争比的策略$ \最大\！对于$ 0 \leqγ<π/3 $和$ \ max \ weft \ {5/2,4 \ big/\ big/\ big（1+2 \ tan（π/4-γ/2）\ big）+ε\ right \ right \} $和对数的建议，以及所有输入量的所有输入量的建议， $ [π/4-γ/2，π/4+γ/2] $，$ 0 \leqγ\leqπ/3 $。此外，我们还提供了$ 5/2 $竞争的策略，还为无限制的向量案例使用对数建议。这些结果应与当前最佳竞争战略FirstFit形成鲜明对比，竞争比率约为27美元。
We consider the online two-dimensional vector packing problem, showing a lower bound of $11/5$ on the competitive ratio of any {\sc AnyFit} strategy for the problem. We provide strategies with competitive ratio $\max\!\left\{2,6\big/\big(1+3\tan(π/4-γ/2)\big)+ε\right\}$ and logarithmic advice, for any instance where all the input vectors are restricted to have angles in the range $[π/4-γ/2,π/4+γ/2]$, for $0\leqγ<π/3$ and $\max\left\{5/2,4\big/\big(1+2\tan(π/4-γ/2)\big)+ε\right\}$ and logarithmic advice, for any instance where all the input vectors are restricted to have angles in the range $[π/4-γ/2,π/4+γ/2]$, for $0\leqγ\leqπ/3$. In addition, we give a $5/2$-competitive strategy also using logarithmic advice for the unrestricted vectors case. These results should be contrasted to the currently best competitive strategy, FirstFit, having competitive ratio~$27/10$.
