关于连续型CNN问题
On the Continuous CNN Problem
摘要：
在（离散）CNN问题中，在线请求显示为$\mathbb{R}^2$中的点。每一个请求都必须在下一个请求出现之前完成。我们有一个服务器，它可以简单地通过将其$x$或$y$坐标与请求对齐来为请求提供服务。在线算法的目标是最小化服务器为服务所有请求而行进的总$L_1$距离。离散版本最著名的竞争比是879（由于Sitters和Stougie）。我们研究了连续版本，其中请求可以在$\mathbb{R}^2$中连续移动，服务器必须连续地服务请求。一个简单的对抗性论证表明，对于连续CNN问题，任何在线算法的竞争比的下限都是3。我们的主要贡献是一个在线算法的竞争比$3+2 \sqrt{3} \approx 6.464$。我们的分析很严密。连续版本推广了离散正交CNN问题，其中每个请求必须是$x$或与前一个请求对齐的$y$。因此，我们的结果改进了以前的最佳竞争比9（由于岩间和米泽）。
英文摘要：
In the (discrete) CNN problem, online requests appear as points in $\mathbb{R}^2$. Each request must be served before the next one is revealed. We have a server that can serve a request simply by aligning either its $x$ or $y$ coordinate with the request. The goal of the online algorithm is to minimize the total $L_1$ distance traveled by the server to serve all the requests. The best known competitive ratio for the discrete version is 879 (due to Sitters and Stougie). We study the continuous version, in which, the request can move continuously in $\mathbb{R}^2$ and the server must continuously serve the request. A simple adversarial argument shows that the lower bound on the competitive ratio of any online algorithm for the continuous CNN problem is 3. Our main contribution is an online algorithm with competitive ratio $3+2 \sqrt{3} \approx 6.464$. Our analysis is tight. The continuous version generalizes the discrete orthogonal CNN problem, in which every request must be $x$ or $y$ aligned with the previous request. Therefore, Our result improves upon the previous best competitive ratio of 9 (due to Iwama and Yonezawa).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
