一种在线冻结标签的优化算法
An Optimal Algorithm for Online Freeze-tag
摘要：
在冻结标签问题中，一个活动的机器人必须唤醒许多冻结的机器人。机器人被视为度量空间中的点，其中主动机器人以恒定速率移动并通过访问其他机器人来激活它们。在问题的（时间依赖的）在线变体中，冻结的机器人直到指定的时间才被发现。Hammar、Nilsson和Rehbison已经证明，对于在线冻结标签，没有在线算法可以实现比$7/3$更好的竞争比，并且询问是否存在任何$O(1)$竞争算法。本文提出了一种基于$(1+\sqrt{2})$的在线时间依赖冻结标签竞争算法，并证明了没有一种算法在每个度量空间上都能达到较低的竞争比。
英文摘要：
In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and activate other robots by visiting them. In the (time-dependent) online variant of the problem, frozen robots are not revealed until a specified time. Hammar, Nilsson, and Persson have shown that no online algorithm can achieve a competitive ratio better than $7/3$ for online freeze-tag, and asked whether there is any $O(1)$-competitive algorithm. In this paper, we provide a $(1+\sqrt{2})$-competitive algorithm for online time-dependent freeze-tag, and show that no algorithm can achieve a lower competitive ratio on every metric space.
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。
