平面上的异步方法：确定性多项式算法
Asynchronous approach in the plane: A deterministic polynomial algorithm
摘要：
在本文中，我们研究的方法的任务的两个移动代理具有相同的有限范围内的视觉和移动异步在平面上。这个任务是在有限的时间内让他们进入彼此的视野范围。代理执行相同的确定性算法，并假定有一个指南针显示的基本方向以及单位测量。另一方面，它们不共享任何全球坐标系统（如GPS），无法通信，并且具有不同的标签。每个代理知道自己的标签，但不知道其他代理的标签或其他代理相对于自己的初始位置。智能体的路线是一系列随后被遍历以实现接近的段。对于每个代理，其路由的计算仅取决于其算法和标签。对手选择两个智能体在飞机上的初始位置，并控制它们中的每一个沿着路线的每一段移动的方式，特别是通过任意改变智能体的速度。确定性接近算法是一种确定性算法，它总是允许两个具有任何不同标签的智能体解决接近任务，而不管对手的选择和行为。接近算法的完整执行的成本是代理在接近完成之前行进的路线的两个部分的长度。令$Δ$和$l$分别为分隔代理的初始距离和最短标签的长度。假设$Δ$和$l$对两个代理都是未知的，是否存在总是以在$Δ$和$l$中为多项式的成本工作的确定性方法算法？在本文中，我们提供了一个肯定的答案，上述问题通过设计这样一个算法。
英文摘要：
In this paper we study the task of approach of two mobile agents having the same limited range of vision and moving asynchronously in the plane. This task consists in getting them in finite time within each other's range of vision. The agents execute the same deterministic algorithm and are assumed to have a compass showing the cardinal directions as well as a unit measure. On the other hand, they do not share any global coordinates system (like GPS), cannot communicate and have distinct labels. Each agent knows its label but does not know the label of the other agent or the initial position of the other agent relative to its own. The route of an agent is a sequence of segments that are subsequently traversed in order to achieve approach. For each agent, the computation of its route depends only on its algorithm and its label. An adversary chooses the initial positions of both agents in the plane and controls the way each of them moves along every segment of the routes, in particular by arbitrarily varying the speeds of the agents. A deterministic approach algorithm is a deterministic algorithm that always allows two agents with any distinct labels to solve the task of approach regardless of the choices and the behavior of the adversary. The cost of a complete execution of an approach algorithm is the length of both parts of route travelled by the agents until approach is completed. Let $Δ$ and $l$ be the initial distance separating the agents and the length of the shortest label, respectively. Assuming that $Δ$ and $l$ are unknown to both agents, does there exist a deterministic approach algorithm always working at a cost that is polynomial in $Δ$ and $l$? In this paper, we provide a positive answer to the above question by designing such an algorithm.
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。
